École d'Été de Probabilités de Saint-Flour

Large Random Matrices: Lectures on Macroscopic Asymptotics

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

Authors: Guionnet, Alice

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About this book

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.

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)

Table of contents (21 chapters)

  • Introduction

    Guionnet, Alice

    Pages 1-4

  • Wigner’s theorem

    Guionnet, Alice

    Pages 7-28

  • Wigner's matrices; more moments estimates

    Guionnet, Alice

    Pages 29-40

  • Words in several independent Wigner matrices

    Guionnet, Alice

    Pages 41-46

  • Concentration inequalities and logarithmic Sobolev inequalities

    Guionnet, Alice

    Pages 49-57

Buy this book

eBook $54.99
price for USA (gross)
  • ISBN 978-3-540-69897-5
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $69.95
price for USA
  • ISBN 978-3-540-69896-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Large Random Matrices: Lectures on Macroscopic Asymptotics
Book Subtitle
École d'Été de Probabilités de Saint-Flour XXXVI – 2006
Authors
Series Title
École d'Été de Probabilités de Saint-Flour
Series Volume
1957
Copyright
2009
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-69897-5
DOI
10.1007/978-3-540-69897-5
Softcover ISBN
978-3-540-69896-8
Series ISSN
0721-5363
Edition Number
1
Number of Pages
XII, 294
Number of Illustrations and Tables
13 b/w illustrations
Topics