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Large Random Matrices: Lectures on Macroscopic Asymptotics

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

  • Alice Guionnet

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

  8. Free probability

    1. Front Matter
      Pages 266-266
    2. Alice Guionnet
      Pages 227-230
    3. Alice Guionnet
      Pages 231-244
    4. Alice Guionnet
      Pages 245-259
  9. Appendix

    1. Front Matter
      Pages 261-261
    2. Alice Guionnet
      Pages 263-265
    3. Alice Guionnet
      Pages 265-275
  10. Back Matter
    Pages 275-301

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

  • Alice Guionnet
    • 1
  1. 1.UMPAEcole Normale Supérieur de LyonLyon Cedex 07France

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-540-69897-5
  • Copyright Information Springer-Verlag Berlin Heidelberg 2009
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-69896-8
  • Online ISBN 978-3-540-69897-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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