Random Matrices EurAsia 2016. - University of Macau · 2016-07-04 · for a class of random band matrices with block structure. Speci cally, we proved the sup-norm delocalization

Random Matrices EurAsia 2016.

08-July to 10 July 2016, at the University of Macau

In view of the major development and interest generated over past 20 years, it was feltthat, an annual workshop on RandomMatrices should be set-up to bring together pure andapplied mathematicians, theoretical and mathematical physicists, statisticians working inmulti-variate statistics, electrical engineers that are concerned with information theory ofwireless communications, from wide geographical locations.This workshop aims to assemble experts on Random Matrix Theory to share their latestresearch achievements, and to enable exchange of ideas on the subject. The hoped-for purpose is to generate synergy leading to collaborative works with mathematicians,engineers from the University of Macau and from China. The participation of Master andPh. D. students from Macau, including, but not limited to, those in Engineering, wouldhopefully further widen their horizon, leading to Post-Doctoral posts and to exchangeswith students of the researchers.Each invited speaker will present their recent research at the workshop, followed by an in-depth discussion on the topic with the members of the Faculty of Science and Technology.

List of SpeakersAlexander Aptekarev (Keldysh Institute, Moscow, Russia)Zhigang Bao (Institute of Science and Technology, Austria)Gordon Blower (University of Lancaster, United Kingdom)Yik-Man Chiang (Hong Kong University of Science and Technology, Hong Kong, China)Avery Ching (Hong Kong University of Science and Technology, Hong Kong, China)Dan Dai (City University of Hong Kong, Hong Kong, China)Victor Didenko (Universitii Brunei Darussalam, Brunei)Engui Fan (Fudan University, Shanghai, China)Peter Forrester (University of Melbourne, Australia)Thomas Guhr (Universitaet Duisberg Essen, Germany)Jesper Ipsen (University of Melbourne, Australia)Eugene Kanzieper (Holon Institute of Technology, Israel)Sergey Ketov (Tokyo Metropolitan University, Japan)Mario Kieburg (Universitaet Bielefeld, Germany)Maria Lapik (Keldysh Institute, Moscow, Russia)Eunghyun Lee (Nazarbayev University, Khazakhstan)Xiang-Dong Li (Academy of Mathematics and Systems Science, Chinese Academy of Sci-ences, China)Dang-Zheng Liu (University of Science and Technology of China, Hefei, China)Jin Song Liu (Academy of Mathematics and Systems Science, Chinese Academy of Sci-ence, China)Thorsten Neuschel (Universit catholique de Louvain, Belgium)Patrick Ng (The University of Hong Kong, Hong Kong, China)

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Maciej Nowak (Mark Kac Complex System Research Center, Jagiellonian University,Poland)Ewa Gudowska-Nowak (Mark Kac Complex System Research Center, Jagiellonian Uni-veristy, Poland)Gregory Schehr (LPTMS, University of Paris-Sud, France)Pragya Shukla (IIT Kharagpur, India)Jack Silverstein (North Carolina State University, North Carolina, USA)Chiu-Yin Tsang (Hong Kong University of Science and Technology, Hong Kong, China)Jacobus Verbaarschot (SUNY at Stony Brook, USA)Dong Wang (National University of Singapore, Singapore)Jian-Feng Yao (The University of Hong Kong, Hong Kong, China)Bin Ye (China University of Mining and Technology, China)Lun Zhang (Fudan University, Shanghai, China)

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Random Matrices EurAsia 2016

(8-10 July)

Venue: E11-G015

Friday, 8 July 2016

8:30-9:00 Registration

9:00-9:15 Opening Remarks

Session 1 Chair: Maciej Nowak

9:15-9:45 Invariant measures, volumes and random lattices

Peter Forrester, University of Melbourne, Australia

9:45-10:15 Concentration inequalities for invariant measures for periodic PDE and RMT Gordon Blower, University of Lancaster, United Kingdom

10:15-10:35 Coffee Break

10:35-11:05 Multiple orthogonal polynomials ensembles

Alexander Aptekarev, Keldysh Institute, Russia

11:05-11:35 May-Wigner stability and geometric Dyson Brownian motion

Jesper Ipsen, University of Melbourne, Australia

11:35-12:05 Local universality in biorthogonal Laguerre ensembles

Lun Zhang, Fudan University, China

12:05-14:00 Lunch

Session 2 Chair: Jacobus Verbaarschot

14:00-14:30 New and Exact Results for the Real, Correlated Wishart Model

Thomas Guhr, Universitaet Duisberg Essen, Germany

14:30-15:00 Generalized Invertibility of Toeplitz plus Hankel Operators Victor Didenko, Universiti Brunei Darussalam, Brunei

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15:00-15:30 Third order phase transitions in RMT and related models

Gregory Schehr, LPTMS, University of Paris-Sud, France

15:30-16:00

Critical edge behavior and the Bessel to Airy transition in the singularly perturbed Laguerre unitary ensemble Dan Dai, City University of Hong Kong, Hong Kong, China


16:20-16:50

On certain eigen-solutions of the Darboux/Heun equation Chiu-Yin Tsang, Hong Kong University of Science and Technology, Hong

Kong, China

16:50-17:20

Rigid local system approach to eigenspaces of special Heun connections

Avery Ching, Hong Kong University of Science and Technology, Hong Kong,

China

17:20-17:50 Delocalization of random block band matrices

Zhi-Gang Bao, Institute of Science and Technology, Austria

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Saturday, 9 July 2016

Session 3 Chair: Peter Forrester

9:00-9:30

Ornstein Uhlenbeck diffusion of hermitian and non-hermitian matrices

unexpected links

Maciej Nowak, Mark Kac Complex System Research Center, Jagiellonian

University, Poland

9:30-10:00

Teichmuller space and some of its applications

Jin-Song Liu, Academy of Mathematics and System Sciences, Chinese

Academy of Sciences, China

10:00-10:30 Universality in the two matrix model with a quadratic potential

Dong Wang, National University of Singapore, Singapore

10:30-11:00 Group Photo & Coffee Break

11:00-11:30

On the Law of Larger Numbers and Functional Central Limit Theorem for Generalized Dyson Brownian Motion Xiang-Dong LI, Academy of Mathematics and System Sciences, Chinese

Academy of Sciences, China

11:30-12:00

Nonequilibrium Properties of Levy Noises

Ewa Gudowska-Nowak, Mark Kac Complex System Research Center,

Jagiellonian University, Poland

12:00-12:30

Galoisian approach to complex oscillation of Hill's equations Yik-Man Chiang, Hong Kong University of Science and Technology,

Hong Kong, China

12:30-14:00 Lunch

Session 4 Chair: Thomas Guhr

14:00-14:30 Random Matrix Theories in Strongly Interacting Gauge Theories

Jacobus Verbaarschot, SUNY at Stony Brook, USA

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14:30-15:00 Bijective Relations between Eigenvalue and Singular Value Statistics

Mario Kieburg, Universitaet Bielefeld, Germany

15:00-15:30 Expanded zero distribution of the Hermite polynomials and GUE

Maria Lapik, Keldysh Institute, Russia

15:30-16:00

The Fredholm determinant representations for some particle systems in the integrable probability Eunghyun Lee, Nazarbayev University, Khazakhstan


16:20-16:50

Moments and Spectral Densities of Singular Value Distributions for Products of Gaussian and Truncated Unitary Random Matrices Thorsten Neuschel, Université catholique de Louvain, Belgium

16:50-17:20 Critical points of polynomials with random zeros

Patrick, Tuen-Wai Ng, The University of Hong Kong, Hong Kong, China

17:20-17:50 Universality in complexity: a random matrix view-point

Pragya Shukla, Indian Institute of Technology Kharagpur, India

19:00 Banquet

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Sunday, 10 July 2016

Session 5 Chair: Dong Wang

8:45-9:15

Large n-limit for Random matrices with External Source with three distinct eigenvalues En-Gui Fan, Fudan University, China

9:15-9:45

Estimating Population Eigenvalues From Large Dimensional Sample Covariance Matrices Jack Silverstein, North Carolina State University, North Carolina, USA

9:45-10:15 Power spectrum analysis of long eigenlevel sequences in quantum chaology

Eugene Kanzieper, Holon Institute of Technology, Israel

10:15-10:45 On singular values for products of two coupled random matrices

Dang-Zheng Liu, University of Science and Technology of China, China


11:05-11:35

Flux-induced scalar potentials in Type IIA strings compactified on rigid Calabi-Yau three-folds Sergey Ketov, Tokyo Metropolitan University, Japan

11:35-12:05

Extreme eigenvalues of large-dimensional spiked fisher matrices with application Jian-Feng Yao, The University of Hong Kong, Hong Kong, China

12:05-12:35 Distinguishing chaotic time series from noise: A random matrix approach Bin Ye, China University of Mining and Technology, China

Abstracts

Multiple orthogonal polynomials ensembles

Alexander AptekarevKeldysh Institute, Moscow, RussiaEmail: [email protected]

Abstract Let µ(x) := (µ1(x), . . . , µd(x)) be a vector of positive measures. For a givenmultiindex n = (n1, . . . , nd) we consider a polynomial Pn(x) of degree |n| := n1 + . . .+np,which satisfies nj orthogonality relations to the degrees of the scalar variable x withrespect to the measure µj, j = 1, . . . , p . Such polynomials always exist and they arecalled multiple orthogonal polynomials. For p = 1 we have usual orthogonal polynomials.We discuss several examples of ensembles of random matrices related to the multipleorthogonal polynomials (namely: random matrix model with external source, two matrixmodel). More attention will be paid to the normal matrix model and to the relationbetween orthogonal polynomials with respect to area measure and multiple orthogonalpolynomials.

Delocalization of random block band matrices

Zhigang BaoInstitute of Science and Technology, AustriaEmail: [email protected]

Abstract For 1D random band matrix, it was conjectured that Anderson transition canbe observed with a threshold W ∼

√N , where W is the bandwidth and N is the matrix

size. More specifically, the conjecture states: for the random band matrices, the systemis delocalized and the local eigenvalue statistics are governed by random matrix statisticsif W

√N , while the system is localized and the local eigenvalue statistics is given by

Poisson statistics if W √N . However, The threshold N has not yet been achieved

from either sides. In this talk, I will introduce a recent result on the delocalization side,for a class of random band matrices with block structure. Specifically, we proved the sup-norm delocalization for random block band matrices with bandwidth W N6/7, usinga combination of a rigorous supersymmetry method and the Green function comparisonmethod. This is a joint work with Laszlo Erdos.

Concentration inequalities for invariant measures for periodic PDE and RMT

Gordon BlowerUniversity of Lancaster, United KindomEmail: [email protected]

Abstract This talk is about the analogy between two types of Hamiltonian systems:periodic PDE and generalized orthogonal ensembles. The partial differential equationsKdV,NLSE and Zhakharov appear in quantum field theory. The purpose of the researchis to understand typical solutions of these PDE; we interpret typical as meaning with large

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probability with respect to a suitably chosen measure, invariant under the flow generatedby the PDE. There is an important analogy between the measures on random matrixensembles and the Gibbs measures for periodic PDE. The concentration inequalities formatrices from the generalized orthogonal ensembles with convex potential resemble thosefrom the typical solutions of the PDE under Gibbs measures. In particular, the eigenvaluesof large matrices from the generalized orthogonal ensemble have properties similar to thoseof the periodic eigenvalues of Hills equations −f ′′+qf = λf where q is periodic and chosento be random and subject to the Gibbs measure of the KdV equation.

Galoisian approach to complex oscillation of Hill’s equations

Yik-Man ChiangHong Kong University of Science and Technology, Hongkong, ChinaEmail: [email protected]

Abstract We demonstrate that complex non-oscillatory solutions (in the sense of Nevan-linna theory) of certain class of Hill equations are among the Liouvillian solutions of anassociated differential equations. We shall establish a full equivalence between the twoviewpoints when the Hill potential is a linear combination of four exponential functions.This Hill equation is closely related to the classical Lame and Mathieu equations. Weshall also discuss new orthogonality found for these non-oscillatory solutions. (This is ajoint work with Guofu Yu).

Rigid local system approach to eigenspaces of special Heun connections

Avery Ching,Hong Kong University of Science and Technology, Hong Kong, ChinaEmail: [email protected]

Abstract The classical hypergeometric equation is an equation with three regular sin-gularities, which is well-studied since the era of Riemann. An obvious generalization ofthe hypergeometric equation would be the Heun equation, which is one with four regularsingularities. However, most methodologies in the study of hypergeometric fails for Heun.In this talk we will clarify the obstruction of relating solutions of a Heun to that of ahypergeometric, and discuss the special case when such an obstruction vanishes. (This isa joint work with Yik-Man Chiang and Chiu-Yin Tsang).

Critical edge behavior and the Bessel to Airy transition in the singularlyperturbed Laguerre unitary ensemble

Dan DaiCity University of Hong Kong, ChinaEmail: [email protected]

Abstract In this paper, we study the singularly perturbed Laguerre unitary ensemble

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Zn(detM)αe−trVt(M)dM, α > 0,

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with Vt(x) = x + t/x, x ∈ (0,+∞) and t > 0. Due to the effect of t/x for varying t,the eigenvalue correlation kernel has a new limit instead of the usual Bessel kernel at thehard edge 0. This limiting kernel involves ψ-functions associated with a special solutionto a new third-order nonlinear differential equation, which is then shown equivalent to aparticular Painleve III equation. The transition of this limiting kernel to the Bessel andAiry kernels is also studied when the parameter t changes in a finite interval (0, d]. Ourapproach is based on Deift-Zhou nonlinear steepest descent method for Riemann-Hilbertproblems.

This a joint work with Shuai-Xia Xu and Yu-Qiu Zhao.

Generalized Invertibility of Toeplitz plus Hankel Operators

Victor DidenkoUniversiti Brunei Darussalam, BruneiEmail: [email protected]

Abstract Let T be the unit circle with the centre at the origin and let a, b ∈ L∞. Thetalk is devoted to generalized invertibility of Toeplitz plus Hankel operators T (a) +H(b)acting on the classical Hardy spaces Hp(T), 1 < p < ∞. After a short survey of knownresults on Fredholmness and the index of such operators, we consider a special case wherethe generating functions a and b satisfy the condition

a(t) a(1/t) = b(t) b(1/t), t ∈ T. (1)

It turns out that in the case at hand an effective description of the structure of the kerneland cokernel of the corresponding operator T (a) + H(b) can be derived. Moreover, thegeneralized inverses of Toeplitz plus Hankel operators with such generating functions canalso be found. The corresponding constructions are based on the Wiener-Hopf factoriza-tion of auxiliary scalar functions. Therefore, such an approach leads to efficient analyticrepresentations of the corresponding generalized inverses.

This talk is based on joint work with Bernd Silbermann [1], [2], [3].

References:

[1] V. D. Didenko and B. Silbermann, Structure of kernels and cokernels of Toeplitzplus Hankel operators, Integral Equations and Operator Theory, 80 (2014), 1–31.

[2] V. D. Didenko and B. Silbermann, Some results on the invertibility of Toeplitzplus Hankel operators, Annalas Academie Scientarium Fennicae, Mathematica, 39(2014), 439–446.

[3] V. D. Didenko and B. Silbermann, Generalized inverses and solution of equationswith Toeplitz plus Hankel operators, Boletin de la Sociedad Matematica Mexicana,Published Online on 7 March, 2016, DOI 10.1007/s40590-016-0101-2, 23pp.

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Large n-limit for Random matrices with External Source with three distincteigenvalues

En-Gui FanFudan University, ChinaEmail: [email protected]

Abstract In this paper, we analyze the large n-limit for random matrix with externalsource with three distinct eigenvalues. And we confine ourselves in the Hermite caseand the three distinct eigenvalues are −a, 0, a. For the case a2 > 3, we establish theuniversal behavior of local eigenvalue correlations in the limit n → ∞, which is knownfrom unitarily invariant random matrix models. Thus, local eigenvalue correlations areexpressed in terms of the sine kernel in the bulk and in terms of the Airy kernel at theedge of the spectrum. The result can be obtained by analyzing 4 × 4 Riemann-Hilbertproblem via nonlinear steepest decent method.

Invariant measures, volumes and random lattices

Peter ForresterUniversity of Melbourne, AustraliaEmail: [email protected]

Abstract The invariant measures on the classical groups of N × N real orthogonal,and complex unitary, matrices were introduced by Hurwitz in 1897, in a paper thatcan reasonably be argued to be the origin of random matrix theory in mathematics.A subsequent development was by Siegel in the mid 40’s who introduced an invariantmeasure on the matrix group SLN(R), and used this to introduce probabilistic methodsinto the study of the geometry of numbers. Later Duke, Rudnik and Sarnak appliedSiegel’s invariant measure to the asymptotic computation of the number of matrices inSLN(Z), with a bounded norm. In this talk these lines of study will be reviewed, andwill be shown to be related to the recent advances in the study of integrable propertiesof random matrix products. Also, some new results relating to the geometry of randomlattices will be presented.

New and Exact Results for the Real, Correlated Wishart Model

Thomas GuhrUniversitaet Duisburg-Essen, GermanyEmail: [email protected]

Abstract The Wishart model is an indispensable tool for the statistical analysis of timeseries of any kind. Applications comprise numerous systems in physics, chemistry, biology,climate research, medicine, finance, telecommunication and other fields. Correlationsbetween the time series are fully incorporated. For the analysis of empirical data, the caseof real time series is the most important one, but unfortunately it poses the most severemathematical problems. In the talk, I will present several new and exact results for thiscase, partly derived with the help of the supersymmetry method. Among other results, weobtained the exact distribution of the smallest eigenvalue as well as an exact result for thespectral density, i.e. the marginal probability density for arbitrary correlation structure.

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We also generalized the last result for the doubly correlated real Wishart model, in whichcorrelations in positions and times are accounted for.

May–Wigner stability and geometric Dyson Brownian motion

Jesper R. IpsenThe University of Melbourne, AustraliaEmail: [email protected]

Abstract We consider the evolution of the finite-time Lyapunov exponents for a matrix-valued generalisation of a geometric Brownian motion. Such processes appear in a varietyof questions in mathematical physics, our main motivation is their relation to a May–Wigner-like stability analysis. For complex matrices the Fokker-Planck equation for theLyapunov exponents happens to coincide with an exactly solvable class of models ofthe Calogero-Sutherland type. The corresponding joint probability distribution describesa biorthogonal ensembles. Some connections to other random matrix models will bediscussed as well.

Power spectrum analysis of long eigenlevel sequences in quantum chaology

Eugene KanzieperHolon Institute of Technology, IsraelEmail: [email protected]

Abstract Fluctuations in quantum spectra are known to exhibit a high degree of univer-sality which reflects the nature – regular or chaotic – of the underlying classical dynamics.Following Berry and Tabor (1977), statistics of level spacings in generic quantum systemswith completely integrable classical dynamics is expected to mimic statistics of waitingtimes in a Poisson point process. For generic quantum systems with completely chaot-ic classical dynamics, Bohigas, Giannoni and Schmit (1984) conjectured that the levelspacing distribution coincides with predictions of the Random Matrix Theory.

Recently, an alternative characterization of eigenvalue fluctuations was suggested byRelano et. al. (2002). Interpreting long eigenlevel sequences as discrete-time randomprocesses, these authors argued that the power spectrum of energy level fluctuationsexhibits the 1/ω behavior for completely chaotic and 1/ω2 behavior for completely regularquantum systems.

In this talk, we present a rigorous theory of the power-spectrum and show that it canbe expressed in terms of Painleve VI function. We also outline the asymptotic (large-N), analysis of the resulting expression to confirm the small–ω behavior reported invarious numerical experiments. Further work is required to analyze behavior of the power-spectrum in the domain ω ∼ O(N) and close to the Nyquist frequency where a descriptionin terms of Painleve V functions is expected to emerge.

This is a joint work with Vladimir Osipov (Lund) and Roman Riser (Holon).

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Flux-induced scalar potentials in Type IIA strings compactified on rigid Calabi-Yau three-folds

Sergey KetovTokyo Metropolitan University, JapanEmail: [email protected]

Abstract I briefly review superstring cosmology, and consider a derivation of exact quan-tum low-energy effective action of type IIA strings compactified on rigid Calabi-Yau s-paces.

Bijective Relations between Eigenvalue and Singular Value Statistics

Mario KieburgUniversitaet Bielefeld, GermanyEmail: [email protected]

Abstract The question about relations between eigenvalues and singular values of a com-plex matrix is a highly non-trivial problem. For an arbitrary fixed matrix, the eigenvaluesand singular values almost only satisfy inequalities which was shown in a series of worksby Schur, Weyl and Horn. The situation is completely different when considering a ran-dom matrix. The additional information via a distribution may yield exact relations inthe form of equalities. Holger Koesters and myself have found that this is indeed truefor bi-unitarily invariant random matrix ensembles, meaning the distribution is invariantunder left and right multiplication of two independent unitary matrices. I will presentthese results and their consequences along non-trivial examples. In particular I will sketchwhat its implications to products of random matrices is.

Expanded zero distribution of the Hermite polynomials and GUE

Maria A. LapikKeldysh Institute, Moscow, RussiaEmail: [email protected]

Abstract

The Fredholm determinant representations for some particle systems in theintegrable probability

Eunghyun LeeNazarbayev University, KhazakhstanEmail: [email protected]

Abstract In the first part of the talk, we review that the probability distribution ofa tagged particles position in the ASEP with step initial condition is represented by aFredholm determinant and it is asymptotically governed by the GUE Tracy-Widom dis-tribution. In the second part, we will introduce some other models Fredholm determinantrepresentations and discuss about the asymptotic behavior of the first particle.

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On the Law of Larger Numbers and Functional Central Limit Theorem forGeneralized Dyson Brownian Motion

Xiang-Dong LiAcademy of Mathematics and Systems Science, Chinese Academy of Sciences, ChinaEmail: [email protected]

Abstract We study the generalized Dyson Brownian motion (GDBM) of an interactingN-particle system with logarithmic Coulomb interaction and general external potentialV . Under reasonable condition on V , we prove the existence and uniqueness of strongsolution to SDE for GDBM. We then prove that the family of the empirical measures ofGDBM is tight on C([0, T ], P (R))and all the large N limits satisfy a nonlinear McKean-Vlasov equation. Inspired by previous works due to Biane and Speicher, Carrillo, McCannand Villani, we prove that the McKean-Vlasov equation is indeed the gradient flow of theVoiculescu free entropy on the Wasserstein space of probability measures over R. Usingthe optimal transportation theory, we prove that if V ′′ ≥ K for some constant K ∈ R,the McKean-Vlasov equation has a unique weak solution. This proves the Law of LargeNumbers and the propagation of chaos for the empirical measures of GDBM. Finally, weprove the Functional Central Limit Theorem for the empirical measure of GDBM towardsthe McKean-Vlasov equation.Joint work with Songzi Li and Yongxiao Xie.

On singular values for products of two coupled random matrices

Dang-Zheng LiuUniversity of Science and Technology of China, Hefei, ChinaEmail: [email protected]

Abstract Consider the product GX of two rectangular complex random matrices coupledby a constant matrix Ω, where G can be thought to be a Gaussian matrix and X is abi-invariant polynomial ensemble. We prove that the squared singular values form abiorthogonal ensemble in Borodin’s sense, and further that for X being Gaussian thecorrelation kernel can be expressed as a double contour integral. When all but finitelymany eigenvalues of ΩΩ∗ are equal, the corresponding correlation kernel is shown to admita phase transition phenomenon at the hard edge in four different regimes as the couplingmatrix changes. Specifically, the four limit kernels in turn are the Meijer G-kernel forproducts of two independent Gaussian matrices, a new critical and interpolating kernel,the perturbed Bessel kernel and the finite coupled product kernel associated with GX.In the special case that X is also a Gaussian matrix and Ω is scalar, such a product hasbeen recently investigated by Akemann and Strahov.

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Teichmuller space and some of its applications

Jin-Song LiuInstitute of Mathematics, Academic of Mathematics and Systems Science, Chinese A-cademy of Sciences, Beijing 100190, P. R. ChinaEmail: [email protected]

Abstract Teichmuller space gives a parametrization of all the complex structures on agiven Riemann surfaces.

In this talk we introduce the basic definitions and results of Teichmuller space. Asits applications, we will provide a rigidity result of the Midscribability Theorem. Fur-thermore, we shall investigate the stability of some inscribable graphs of the Riemannsphere.

Moments and Spectral Densities of Singular Value Distributions for Productsof Gaussian and Truncated Unitary Random Matrices

Thorsten NeuschelUniversite catholique de Louvain, BelgiumEmail: [email protected]

Abstract We study moments and densities of limiting distributions of singular values oflarge dimensional matrix products composed of independent complex Gaussian (complexGinibre) and truncated unitary matrices which are taken from Haar distributed unitarymatrices with appropriate dimensional growth. It turns out that the moments can beexpressed by Jacobi polynomials with varying parameters whereas the densities admitexplicit integral representations with elementary integrands. The derivation is based onan approach to obtain complex integral representations for densities of measures whoseStieltjes transforms satisfy algebraic equations of a certain type.

Critical points of polynomials with random zeros

Patrick, Tuen Wai NgThe University of Hong Kong, Hong Kong, ChinaEmail: [email protected]

Abstract The study of zero distribution of random polynomials has a long history and iscurrently a very active research area. Traditionally, the randomness in these polynomialscomes from the probability distribution followed by their coefficients. One can introducerandomness in the zeros (instead of the coefficients) of polynomials, and then investigatethe locations of their critical points (relative to these zeros). Such a study was initiatedby Rivin and the late Schramm in 2001, but only until 2011, Pemantle and Rivin pro-posed a precise probabilistic framework of it which will first be explained in this talk.Following this framework, we will consider the problem of finding the zero distributions ofthe derivatives of random polynomials with i.i.d. zeros following a common distributionsupported on a subset of the complex plane. Recently, Sean O’Rourke applied the sameframework to study critical points of characteristic polynomial of a random matrix drawnfrom one of the compact classical matrix groups.

This is a joint work with Pak-Leong Cheung, Jonathan Tsai and Phillip Yam and thework was supported by the RGC grant HKU 704611P and HKU 703313P.

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Ornstein Uhlenbeck diffusion of hermitian and non-hermitian matrices unex-pected links

Maciej A. NowakMark Kac Complex System Research Center, Jagiellonian University, PolandEmail: [email protected]

Abstract

Nonequilibrium properties of Levy noisesEwa Gudowska-NowakMark Kac Complex System Research Center, Jagiellonian University, PolandEmail: [email protected]

Abstract

Third order phase transitions in RMT and related models

Gregory SchehrLPTMS, CNRS-Univ. Orsay, Paris-Sud, FranceEmail: [email protected]

Abstract The statistical properties of the largest eigenvalue of a random matrix areof interest in diverse fields such as in the stability of large ecosystems, in disorderedsystems and related stochastic growth processes, in statistical data analysis and even instring theory. In this talk, I will present the theory of extremely rare fluctuations (largedeviations) of the largest eigenvalue using a Coulomb gas approach. I will discuss inparticular the third-order phase transition which separates the left tail from the righttail, a transition akin to the so-called Gross-Witten-Wadia phase transition found in 2-dlattice quantum chromodynamics. I will also discuss the occurrence of similar third-ordertransitions in various physical problems, including non-intersecting Brownian motions andstochastic growth models in the Kardar-Parisi-Zhang (KPZ) universality class.

Universality in complexity: a random matrix view-point

Pragya ShuklaDepartment of Physics, Indian Institute of Technology, IndiaEmail: [email protected]

Abstract The complexity of a system, in general, makes it difficult to determine some oralmost all matrix elements. The lack of accuracy acts as a source of randomness for thematrix elements which are also subjected to an external potential due to existing systemconditions. The operator can then be described by a system dependent random matrix.The fluctuation of accuracy due to varying system conditions leads to diffusion of thematrix elements. We show that, for single-well potentials, the diffusion can be describedby a common mathematical formulation where system information enters through a singleparameter. This suggests possible classification of complex systems in an infinite rangeof universality classes characterized just by a single parameter and the nature of global

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physical constraints. It seems to indicate a web of connection hidden underneath complexsystems (even beyond delocalized wave regime) ranging as widely as quantum world ofnano-systems on one hand to classical world of complex networks on the other hand.

Estimating Population Eigenvalues From Large Dimensional Sample Covari-ance Matrices

Jack W. SilversteinDepartment of Mathematics, North Carolina State University, USAEmail: [email protected]

Abstract Let Bn = (1/N)T 1/2n XnX

∗nT

1/2n where Xn = (Xi,j) is n×N with i.i.d. complex

standardized entries, and T 1/2n is a Hermitian square root of the nonnegative definite

Hermitian matrix Tn. This matrix can be viewed as the sample covariance matrix of Ni.i.d. samples of the n dimensional random vector T 1/2

n (Xn)·1, the latter having Tn for itspopulation covariance matrix. Quite a bit is known about the behavior of the eigenvaluesof Bn when n and N are large but on the same order of magnitude. These resultsare relevant in situations in multivariate analysis where the vector dimension is large,but the number of samples needed to adequately approximate the population matrix (asprescribed in standard statistical procedures) cannot be attained. Work has been donein estimating the eigenvalues of Tn from those of Bn. This talk will introduce a methoddevised by X. Mestre, and will present an extension of his method to another ensembleof random matrices important in wireless communications.

On certain eigen-solutions of the Darboux/Heun equation

Chiu-Yin TsangDepartment of mathematics, Hong Kong University of Science and TechnologyEmail: [email protected]

Abstract The Darboux equation (1882) was a generalization of both Picard’s and Her-mite’s equations. All these equations are generalizations of the well-known Lame equation(1837). The equation was rediscovered by Treibich and Verdier in the 1980s concerning ithaving finite-gap property in an algebraic geometric characterization. The equation is a(doubly periodic) torus version of the Heun equation which lives on the Riemann sphere.In this talk, we will derive some series expansion solution of the Darboux/Heun equationand discuss the orthogonality relations between the eigen-solutions (terminating seriessolutions) of the Darboux/Heun equation. This is a joint work with Yik-Man Chiang andAvery Ching.

Random Matrix Theories in Strongly Interacting Gauge Theories

Jacobus VerbaarschotDepartment of physics and Astronomy, Stony Brook University, USAEmail: [email protected]

Abstract We give an introduction to random matrix theories and their applications tostrongly interacting gauge theories. We start with a review of the classification of random

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matrix theories in terms of anti-unitary symmetries and symmetric spaces. Universalproperties of eigenvalue spectra of random matrices are discussed and explained in termsof spontaneous symmetry breaking of supersymmetric sigma models. Connections withintegrable systems are made and are illustrated with applications nonhermitian randommatrix ensembles.

Universality in the two matrix model with a quadratic potential

Dong WangNational University of Singapore, SingaporeEmail: [email protected]

Abstract A two matrix model is defined by the joint probability distribution function ofrandom Hermitian matrices M1 and M2

P (M1,M2) ∝ exp (−Tr(V (M1) +W (M2)− τM1M2)) .

In this talk, we assume that V (x) = a2x2, and V is a general analytic function. We consider

the local statistics of the eigenvalues of M1, as the dimension goes to ∞. As part of ourresult, we confirm that the phase transition found in [Duits-Geudens] with qartic V holdsuniversally for a large class of potential function V. We also find new phase transitionphenomena for different types of V, especially for V that is not an even function.

This is joint work with Tom Claeys, Arno Kuijlaars, and Karl Liechty.

Extreme eigenvalues of large-dimensional spiked Fisher matrices with appli-cation

Jeff YaoDepartment of Statistics and Actuarial Science, The University of Hong Kong, ChinaEmail: [email protected]

Abstract Consider two p-variate populations, not necessarily Gaussian, with covariancematrices Σ1 and Σ2, respectively. Let S1 and S2 be the corresponding sample covariancematrices with degrees of freedom m and n. When the difference ∆ between Σ1 andΣ2 is of small rank compared to p,m and n, the Fisher matrix S := S−12 S1 is called aspiked Fisher matrix. When p,m and n grow to infinity proportionally, we establish aphase transition for the extreme eigenvalues of the Fisher matrix: a displacement formulashowing that when the eigenvalues of ∆ (spikes) are above (or under) a critical value,the associated extreme eigenvalues of S will converge to some point outside the supportof the global limit (LSD) of other eigenvalues (become outliers); otherwise, they willconverge to the edge points of the LSD. Furthermore, we derive central limit theorems forthose outlier eigenvalues of S. The limiting distributions are found to be Gaussian if andonly if the corresponding population spike eigenvalues in ∆ are simple. Two applicationsare introduced. The first application uses the largest eigenvalue of the Fisher matrix totest the equality between two high-dimensional covariance matrices, and explicit powerfunction is found under the spiked alternative. The second application is in the fieldof signal detection, where an estimator for the number of signals is proposed while thecovariance structure of the noise is arbitrary.

This is a joint work with Miss Qinwen Wang (The University of Pennsylvania).

16

Distinguishing chaotic time series from noise: A random matrix approach

Bin YeChina University of Mining and Technology, ChinaEmail: [email protected]

Abstract Deterministically chaotic systems can often give rise to random and unpre-dictable behaviors which make the time series obtained from them to be almost indis-tinguishable from noise. Motivated by the fact that data points in a chaotic time serieswill have intrinsic correlations between them, we propose a random matrix theory (RMT)approach to identify the deterministic or stochastic dynamics of the system. We showthat the spectral distributions of the correlation matrices, constructed from the chaotictime series, deviate significantly from the predictions of random matrix ensembles. On thecontrary, the eigenvalue statistics for a noisy signal follow closely those of random matrixensembles. Our numerical results also indicate that the approach is to some extent robustto additive observational noise which pollutes the data in many practical situations. Thusour approach is efficient in recognizing the chaotic dynamics underlying the evolution ofthe time series.

Local universality in biorthogonal Laguerre ensembles

Lun ZhangSchool of Mathematical Sciences, Fudan University, ChinaEmail: [email protected]

Abstract In this talk, we consider n particles 0 ≤ x1 < x2 < · · · < xn < +∞, distributedaccording to a probability density function of the form

1

Zn

∏1≤i<j≤n

(xj − xi)∏

1≤i<j≤n

(xθj − xθi

) n∏j=1

xαj e−xjdxj, α > −1,

where Zn is the normalization constant and θ = M ∈ N = 1, 2, . . .. This distribu-tion arises in the context of modeling disordered conductors in the metallic regime, andcan also be realized as the distribution for squared singular values of certain triangularrandom matrices. We give a double contour integral formula for the correlation kernel,which allows us to establish universality for the local statistics of the particles, namely,the bulk universality and the soft edge universality via the sine kernel and the Airy k-ernel, respectively. In particular, our analysis also leads to new double contour integralrepresentations of scaling limits at the origin (hard edge), which are equivalent to thosefound in the classical work of Borodin. Further properties of the hard-edge scaling limitswill be presented if time permitted.

17

0

Student Affairs Office (SAO) - Student Resources and Services Section (SRS)

Postgraduate House (PGH)

S1 Hostel Handbook

Table of Contents

Transportation ......................................................................................................................................... 1

Procedures of move-in and move-out .................................................................................................... 7

Cards ........................................................................................................................................................ 8

Things to be prepared before moving-in ................................................................................................ 9

Facilities ................................................................................................................................................. 10

Services .................................................................................................................................................. 11

Important points to note ....................................................................................................................... 11

Safety issue ............................................................................................................................................ 12

General rules ......................................................................................................................................... 12

Contact points ....................................................................................................................................... 13

Appendix................................................................................................................................................ 14

1 Updated on 18/02/2016

Transportation

Private vehicles are allowed to enter the University of Macau (UM) campus and travel only in the

designated area. Public transportation arrangement for entering the campus is as follows:

1. Taxi

Taxis are permitted to enter the campus and the taxi fares are based on a flag-down fare and the

distance travelled.

2. Public Bus

There are FOUR public buses connecting the campus and the Macau Peninsula / the Taipa.

a) Route number: 72

Operation hours: Monday – Sunday, from 6:00 am – 12:15 am

Bus frequency: Every 8 – 15 minutes

Bus fare: MOP2.8

2 Updated on 18/02/2016

Method of transferring to 72 from other public bus routes

From Bus Route Transferring Bus Stop

Barrier Gate

(Gong Bei Border)

25X Av. Dr. Sun Yat Sen / Rua De Lagos

30 Rotunda Dr. Carlos A.C.P. D’Assumpcao

COTAI Frontier Post

(Lotus Border)

21A, 25,

26A, 50

Cross the pedestrian bridge to Bus Stop of “Av. Dr. Sun Yat

Sen / Rua De Lagos”

Macau International Airport MT2



N2 Rotunda Dr. Carlos A.C.P. D’Assumpcao

Macau Maritime Ferry

Terminal 28A Av. Dr. Sun Yat Sen / Rua De Lagos

Taipa Temporary Ferry

Terminal

MT2



N2 Rotunda Dr. Carlos A.C.P. D’Assumpcao

3 Updated on 18/02/2016

b) Route number: 73



Bus fare: MOP4.2 – From UM Terminal to Macau Peninsula

MOP2.8 – From Rotunda Marginal/Zonas Ecológicas to UM Terminal

4 Updated on 18/02/2016

c) Route number: 71



Bus fare: MOP4.2 – From UM Terminal to Macau Peninsula

MOP2.8 – From any stops at UM Campus to UM Terminal

5 Updated on 18/02/2016

Method of transferring to 73 and 71 from other public bus routes

From Bus Route Transferring Bus Stop

Barrier Gate

(Gong Bei Border)

3, 3A, 3X, 10, 10B, 10X, 25X, 30

Praca Ferreira Amaral

Macau Maritime Ferry

Terminal 10A, 28A Praca Ferreira Amaral

d) Route number: 71X

Operation hours: Monday – Friday (except Public Holidays),

from 7:30 am – 10:00 am; 5:00 pm – 8:00pm

Bus frequency: Every 15 minutes

Bus fare: MOP2.8

6 Updated on 18/02/2016

3. Midnight Shuttles

Midnight shuttles provide connection between the campus and the Taipa downtown. The operation

hours are every day from 12 am – 6:40 am. Please present your Room Key Card when boarding, the

service runs on “first come, first served” basis while NO standing is allowed. In case you have

encountered any problem with the overnight inter-campus shuttle bus, please call our Security Team

at 8822 4126.

From Edificio do Lago From UM Postgraduate House

Departure Route Departure Route

00:00

Edificio do Lago ↓

Rotunda Dr. Carlos A.C.P. D’Assumpcao Bus Stop

↓ UM – area between N21 &

N22 ↓

UM – Postgraduate House

00:20

UM – Postgraduate House ↓ ↓

Rotunda Dr. Carlos A.C.P. D’Assumpcao Bus Stop

↓ ↓

Edificio do Lago

00:40 01:00

01:20 01:40

02:00 02:20

02:40 03:00

03:20 03:40

04:40 05:00

05:20 05:40

06:00 06:20

06:40

5. Campus Loop Service In view that the campus covers a total area of 1 km² and it is consisted of more than 80 buildings, our staff, students and guests can make use of the campus loop service, which operates from Mondays to Sundays, to travel between different buildings on campus. Please present your Room Key Card when boarding, the service runs on “first come, first served” basis while NO standing is allowed.

Please refer to the website of the Security and Transport Section (STS) for the campus loop service schedule and route, as well as campus transportation updates http://www.umac.mo/sts/svc_transportation.html

In case of any inconsistency about the transportation information between this handbook and the website of STS, the website of STS shall prevail.

http://www.umac.mo/sts/svc_transportation.html

7 Updated on 18/02/2016

Procedures of move-in and move-out

Move-in

1. Bring the following documents to the reception at PGH – S1, G/F, Room G005 #.

- A copy of your personal identification card / passport

- The accommodation confirmation email sent by SRS

2. Present the aforementioned documents to the receptionist.

3. Fill in the required information and sign in the Postgraduate House -S1 Hostel Registration Form*.

4. Settle your accommodation fee (if any) upon move-in. Kindly note that the accommodation fee

is non-refundable.

5. Receptionist will provide the “Room Key Card” and “Facility Access Card” to you.

# Location is shown on the “PGH Facilities Map”.

* For the resident whose stay period is 14 days or beyond, please return the registration form to

the reception at PGH – S1, G/F, Room G005# within 3 days of your move-in day. If there is no

receipt, it is considered that your room equipment is in good condition and you should bear the

responsibility of any damage to the equipment.

Move-out

1. Please approach to the reception at PGH – S1, G/F, Room G005# for processing the move-out

procedure.

2. All move-out procedure is required to be finished on or before 12 noon at the move-out day.

3. Any late move-out or extension of stay will need to be requested to SRS Student Housing / S1

Reception at least 1 working day prior to the originally proposed move-out day. Otherwise,

exceeding move-out times may result in a special charge of 1 night accommodation being applied

to the bill. Any request is subject to approval from SRS Student Housing and room availability.

4. Clean up your room before moving out.

5. No personal belonging or garbage should be left in your room. Otherwise, cleaning fee and

garbage removal fee will be charged.

6. Please settle the payable fee (if any) of any damage or lost for the in-room equipment. Please

note that all the payable fees are non-refundable.

7. Return your “Room Key Card” and “Facility Access Card” to the receptionist.


8 Updated on 18/02/2016

Cards

Bear in mind to bring your “Room Key Card” and “Facility Access Card” with you at all time, and not to lose or damage those cards. Replacement for the “Room Key Card” incurs a fee of MOP20, while it is MOP50 for the “Facility Access Card”. If you forget to bring your “Room Key Card” or are locked out of your room, please contact the reception to help you opening your room door. A fee of MOP10 will be charged. In addition, if you would like to invite your guest to visit PGH facilities and your own room, you or your guests must submit an application to the reception for a Visitor Pass of PGH. The visiting hours are in accordance with the non-quiet hours of PGH, which are from 7am to 10pm. The applying visitors must return the Visitor Pass to the reception before leaving PGH. No visitor is permitted to stay in PGH after visiting hours.

Room Key Card Facility Access Card

Visitor Pass

9 Updated on 18/02/2016

Things to be prepared before moving-in Documents needed for move-in

Please prepare the following documents for the move-in procedure.

- A copy of your personal identification card / passport

- The accommodation confirmation email sent by SRS

Personal necessities

Rooms in S1 Hostel are fully furnished, internet-connected, air-conditioned

and ensuite bathroom. Meanwhile, PGH is fully committed to protecting our

shared environment, so green practices are implemented, amenities like

shower gel, shampoo, tooth brush, tooth paste are required to be obtained in the reception if

necessary.

Electrical adapter

The voltage in Macau is 220 volts and the type of socket in the PGH contains three holes in

rectangular shape, forming an isosceles triangle. It is suggested to bring your own electrical

adapters.

Network cable

If you want to access internet or get WI-FI access in your room, please approach

to the reception for borrowing the internet cable, the user manual, or getting

the WI-FI password. Please note that in some of the rooms, the internet

connection sockets are hidden behind the furniture.

Telephone

There is no telephone provided in the room. Please prepare your mobile phone for contact, if

necessary. Major Macao mobile networks are installed in the new campus. If you are using a SIM

card which is from the local mobile service provider, please be reminded to choose "manual"

when selecting a mobile network mode so as to avoid roaming since the campus is close to

Mainland China.

10 Updated on 18/02/2016

Facilities

Facilities Location # Opening hours Remarks

Postgraduate House

Laundry PGH – S1 G/F 24 hours

Washing machines are provided to PGH residents to wash and dry the clothes. Please note that washing powder is NOT provided.

Drying Rooms Each floor of PGH –

S1, except G/F 24 hours ---

Pantries Each floor of PGH –

S1 24 hours

Fridges, microwave oven and water dispensers are available in the pantries.

Fitness Room, Badminton, and

Table Tennis Court PGH – S3, G/F, G021

Mon – Sun 7 am – 11 pm

Free of charge

Study Room Television Room

PGH – S2, G/F 24 hours ---

University of Macau Campus

Medical Center Sports Complex N8

G/F, G002

Mon – Thu: 9 am – 1 pm,

2:30 pm – 5:45 pm Fri:

9 am – 1 pm, 2:30 pm – 5:30 pm

Sat: 9 am – 1 pm

Service: Medical consultation Nursing and first aid Measurement of height and weight Blood pressure Body fat percentage Tel: 8822 4123

“Fortune Inn” Chinese Restaurant

Guest House N1, G/F


5:30 pm – 10:30 pm ---

Pacific Coffee Wu Yee Sun Library

E2 (North Wing), G/F


---

Canteen “Food Paradise”

Central Teaching Building E5, G/F

Mon – Sun 8:00 am – 8:00 pm

---

7-Eleven Central Teaching Building E6, G/F

24 hours ---

Circle K Staff Quarters S24,

G/F 24 hours ---

University Mall A mini shopping mall which consists of dining and retail outlets such as pharmacy, bank, laundry,

supermarket, bakery, restaurant, book store, travel agency, etc.

Pharmacy University Mall S8,

G/F, G015 Mon – Sun:

10 am – 8 pm ---

Bank of China University Mall S8,

G/F, G012 Mon – Fri

10 am – 5:30 pm ---

Clean Living Laundry University Mall S8,

G/F, G011

Tue – Sun 10 am – 2 pm, 3 pm – 6 pm

It is chargeable. For the price, please refer to the laundry company.

Supermarket University Mall S8, G/F, G001 & G003

Mon – Sun 8:30 am – 11 pm

Chargeable snacks, fruits, beverages and daily necessities

11 Updated on 18/02/2016

are available in the Service Centre.

“Red Forest” Restaurant

University Mall S8, 1/F, 1009


---

“Padaria da Guia” Bakery

University Mall S8, G/F, G013


---

Azucar University Mall S8,

G/F, G014

Mon – Fri 12 pm – 9 pm

Sat – Sun 12 pm – 7pm

Serves snacks, Chinese and Western desserts

“Old Macau” Restaurant

University Mall S8, 1/F, 1001


---


There are some more campus dining and retail outlets which are not listed in the above table. For

campus dining and retail outlets updates, please visit the website of the Campus

Services Section (CS) http://www.umac.mo/cs/U-Mall/Shopping%20Mall_E.html

In case of any inconsistency about the dining and retail outlets information between

this handbook and the website of CS, the website of CS shall prevail.

Services

Weekly towel and garbage handling service

The handling service is carried on every Monday and Thursday.

Bi-weekly bathroom cleaning service

The cleaning service is carried on a bi-weekly basis and the schedule will be posted on the notice

board on each residential floor.

Repair and maintenance service

Please approach to the reception at PGH – S1, G/F, Room G005# if your room needs any

equipment maintenance.


Important points to note Internet access

You can access the Internet in your room by using internet cable (please bring your own internet)

or WI-FI. Please note that in some of the rooms, the internet connection sockets are hidden

behind the furniture.

Noise level

The period from 10 pm – 7 am is regarded as the quiet hours of PGH. You are expected to behave

in a mature and responsible manner. Please do not create noise nuisance and disturb other

residents.

http://www.umac.mo/cs/U-Mall/Shopping%20Mall_E.html

12 Updated on 18/02/2016

Smoking

Smoking is prohibited within the entire PGH complex except in specified smoking zones.

Alcohol

Possession or drinking of alcohol in PGH is prohibited.

Safety issue Guest identification

For identification issue, you are required to use your Facility Access Card to open the gate

when you are entering into PGH buildings. Please also notice that the security guards may also

require you to present your PGH Room Key Card or identification document(s) at the lobby.

Fire safety

An evacuation plan for emergency can be found behind your room door. Please read it carefully.

In case of a fire, keep calm and escape from the building via the nearest exit.

Emergency

In case of an emergency, please first seek help from the security guard nearby or contact the

Reception, contact number: 8822 2531 / 6353 1156. The number of calling police, ambulance

and fire station in Macau is 999. Please also inform the security guard or reception after calling

for emergency.

# Location will be shown on the “PGH Facilities Map”.

General rules The following behaviors are considered as disciplinary offences and are prohibited in PGH. They apply

to all residents, temporary residents and visitors. For details, please refer to the Postgraduate House

Resident Rules.

a) Entering PGH with hazardous articles and substances, forbidden medicine or drugs;

b) Bringing pets into or keeping pets in PGH;

c) Bringing visitors into PGH during non-visiting hours or without prior approved application from

the Reception/ Management Company/ SRS;

d) Entering rooms of the opposite sex;

e) Smoking in PGH, except in the specified smoking zones;

f) Drinking or possession of alcohol or alcohol content beverages in PGH, except with prior written

approval by the Vice Rector (Student Affairs);

g) Cooking in rooms of PGH, except in pantries or kitchens;

h) Lighting fire;

i) Making noise;

j) Throwing objects out into the air;

k) Improper treatment of garbage;

l) Duplicating room cards/ keys without official authorization;

13 Updated on 18/02/2016

m) Damaging public facilities or the appearance (exterior and interior) and integrality of the rooms

(including but not limited to dirtying, writing, drawing, drilling holes, putting nail or posting any

items on the wall) or altering their functions;

n) Moving, exchanging or damaging the furniture or equipment in rooms or public areas (including

but not limited to dirtying, writing, drawing, drilling holes, putting nail or posting any items on the

furniture) or altering their functions;

o) Entering facility/ equipment room, opening facility/ equipment control box or adjusting facility/

equipment without official authorization;

p) Unauthorized occupation of public areas;

q) Behaviors that cause harassment for other PGH residents;

r) Not settling residence fees, required fees or penalty before payment deadline;

s) Absent from the disciplinary meeting without a justified reason;

t) Behaviors that jeopardize other students’ personal and property safety;

u) Behaviors that severely affect the normal operation and order of the PGH.

Contact points S1 Hostel Reception

- Responsible for performing the S1 Hostel move-in/out procedures, access control and issuing

room key card, housekeeping, maintenance and repairs.

Office hours: 24-hour and 7-day operation (including public holidays)

Location: PGH – S1, G/F, Room G005

Contact number: 8822 2531, 6353 1156

The Student Resources and Services Section – PGH Student Housing

- Responsible for the application, allocation and arrangement of the PGH accommodation

Office hours: Monday – Thursday, 9:00 am – 5:45 pm

Friday, 9:00 am – 5:30 pm

(Excluding public holidays)

Location: PGH - S3, G/F, Room G002

Contact number (office hour): 8822 8014, 8822 9911

Fax: 8822 2371

Email: [email protected]

All the locations are shown in the “PGH Facilities Map”.

14 Updated on 18/02/2016

Appendix The PGH Facilities Map (PGH-S1 ground floor)

Operating Hours of the entrance:

Main Entrance: 24 hours each day

Restricted Entrance: 9am to 11pm each day

Main

Restricted

Entrance

15 Updated on 18/02/2016

The PGH Facilities Map (PGH-S1 Residential floor)

Pantry

Clothes Hanging Area

Rubbish Room

16 Updated on 18/02/2016

Public Bus Stop (71, 72, 73 & 71X)

Medical Center of University of Macau (S8)

Circle K (S24)

7-Eleven (E6)

S1 Hostel