Detailed information about the course

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Title

Random matrices and their applications

Dates

20 - 23 août 2014

Organizer(s)

Prof. Christian Mazza, Fribourg

Speakers

Prof. Charles Bordenave, University of Toulouse, Prof. Alice Guionnet, MIT and ENS Lyon, Prof. Jamal Najim, University of Marne La Vallée

Description

Les modèles classiques de matrices aléatoires sont apparus en physique il y a quelques années; les probabilistes en ont par la suite étudié différents aspects (lois des valeurs propres, processus associés aux valeurs propres). La recherche actuelle comporte de nombreuses facettes, allant de la géométrie à l’analyse fonctionnelle. On trouve par ailleurs des modèles de matrices aléatoires en biologie et en statistique. Le cours va consister à donner les bases mathématiques de la théorie des matrices aléatoires, et de présenter de nouvelles questions qui se posent actuellement dans diverses applications (réseaux de communication sans fil ou statistique).

 

Charles Bordenave (University of Toulouse): Spectrum of sparse random graphs

Unimodular  graphs are the natural limits of finite graph sequences with uniformly bounded degrees. For these graphs, we will define a proper notion of spectrum and study its properties. We will put the emphasis on the study of the regularity of the spectrum and the study of its atoms. Our main examples will come from percolation graphs and classical random graphs. We will also discuss some connections with random matrices.

 

Alice Guionnet (MIT and ENS Lyon): Basics on Random Matrices

In this course we will discuss the properties of Wigner matrices, that is Herimtian matrices with independent entries modulo the symmetry constraint. We will first investigate the macroscopic properties such as the mean asymptotic behaviour of the eigenvalues, and then the local properties such as  the fluctuations of the spacing between two eigenvalues. We will finally review some open problems.

 

Jamal Najim (University of Marne La Vallée): Large random matrices and applications to statistics and electrical engineering

In this course, we shall present random matrix models of interest in electrical engineering and statistics and study their properties in the large dimensional regime. After the mathematical framework is set up, we will describe applications of  large random matrices to wireless communication, statistical signal processing and statistics. We will also present areas  of current interest where the presented techniques are relevant.

Location

Ovronnaz

Information

homeweb.unifr.ch/mazzac/Pub/Ovronnaz2014.htm

Expenses

Doctorant CUSO chambre double: 190 CHF
Doctorant CUSO chambre simple: 250 CHF
Post-doctorant CUSO chambre double: 300 CHF
Post-doctorant CUSO chambre simple: 350 CHF
Professeur CUSO chambre double: 400 CHF
Professeur CUSO chambre simple: 450 CHF
Non CUSO universitaire chambre double:  500 CHF
Non CUSO universitaire chambre simple: 550 CHF

Registration

Prof. Christian Mazza, Fribourg

Places

15

Deadline for registration 20.08.2014
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