Overview

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.

Full Product Details

Author:   Alice Guionnet
Publisher:   Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
Imprint:   Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Edition:   2009 ed.
Volume:   1957
Dimensions:   Width: 15.50cm , Height: 1.60cm , Length: 23.50cm
Weight:   0.980kg
ISBN:  

9783540698968

ISBN 10:   3540698965
Pages:   294
Publication Date:   25 March 2009
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Wigner matrices and moments estimates.- Wigner#x2019;s theorem.- Wigner's matrices; more moments estimates.- Words in several independent Wigner matrices.- Wigner matrices and concentration inequalities.- Concentration inequalities and logarithmic Sobolev inequalities.- Generalizations.- Concentration inequalities for random matrices.- Matrix models.- Maps and Gaussian calculus.- First-order expansion.- Second-order expansion for the free energy.- Eigenvalues of Gaussian Wigner matrices and large deviations.- Large deviations for the law of the spectral measure of Gaussian Wigner's matrices.- Large Deviations of the Maximum Eigenvalue.- Stochastic calculus.- Stochastic analysis for random matrices.- Large deviation principle for the law of the spectral measure of shifted Wigner matrices.- Asymptotics of Harish-Chandra-Itzykson-Zuber integrals and of Schur polynomials.- Asymptotics of some matrix integrals.- Free probability.- Free probability setting.- Freeness.- Free entropy.- Basics of matrices.- Basics of probability theory.

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)

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)

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