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© 2009

Large Random Matrices: Lectures on Macroscopic Asymptotics

École d'Été de Probabilités de Saint-Flour XXXVI ¿ 2006

Book

Part of the Lecture Notes in Mathematics book series (LNM, volume 1957)

Also part of the Ecole d'Eté Probabilit.Saint-Flour book sub series (LNMECOLE, volume 1957)

Table of contents

  1. Front Matter
    Pages I-XII
  2. Alice Guionnet
    Pages 1-4
  3. Wigner matrices and moments estimates

    1. Front Matter
      Pages 5-5
    2. Alice Guionnet
      Pages 7-28
    3. Alice Guionnet
      Pages 29-40
  4. Wigner matrices and concentration inequalities

    1. Front Matter
      Pages 47-48
    2. Alice Guionnet
      Pages 59-64
  5. Matrix models

    1. Front Matter
      Pages 89-91
    2. Alice Guionnet
      Pages 93-107
    3. Alice Guionnet
      Pages 109-118
    4. Alice Guionnet
      Pages 121-145
  6. Eigenvalues of Gaussian Wigner matrices and large deviations

    1. Front Matter
      Pages 147-148
    2. Alice Guionnet
      Pages 159-162
  7. Stochastic calculus

About this book

Introduction

Random matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the asymptotic distribution of matrices, which is naturally defined in the context of free probability and operator algebra.
The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Maury Bramson and Steffen Lauritzen.

Keywords

Eigenvalue Graph Matrix Matrix Theory Measure Probability theory algebra

Authors and affiliations

  1. 1.UMPAEcole Normale Supérieur de LyonLyon Cedex 07France

Bibliographic information

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Reviews

From the reviews: “This book is a set of lecture notes on eigenvalues of large random matrices. … useful to all mathematicians and statisticians who are interested in Wigner matrices. … In summary, the book is very much worth perusal.” (Vladislav Kargin, Mathematical Reviews, Issue 2010 d)