Guionnet, Alice.

Large random matrices : lectures on macroscopic asymptotics : École d'été de probabilités de Saint-Flour XXXVI--2006 / Alice Guionnet. - Berlin : Springer, ©2009. - 1 online resource (xii, 294 pages) : illustrations - Lecture notes in mathematics, 1957 0075-8434 ; . - Lecture notes in mathematics (Springer-Verlag) ; 1957. .

Includes bibliographical references (pages 275-285) and index.

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.

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.


English.

9783540698975 3540698973 1282127934 9781282127937 9783540698968 3540698965

10.1007/978-3-540-69897-5 doi

978-3-540-69896-8 Springer http://www.springerlink.com

2008943975

GBA902914 bnb

014870297 Uk


Random matrices.
Random matrices.
Random matrices.


Electronic books.

QA3 / .L28 no.1957

512.9434

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