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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.
List of contents
Notation.- Introduction.- Part I Wigner matrices and moments estimates.- Part II Wigner matrices and concentration inequalities.- Part III Matrix models.- Part IV Eigenvalues of Gaussian Wigner matrices and large deviations.- Part V Stochastic Calculus.- Part VI Free probability.- Part VII Appendix.- References.- Index.
Summary
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.
Report
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)
