Large random matrices : lectures on macroscopic asymptotics : École d'été de probabilités de Saint-Flour XXXVI--2006 / Alice Guionnet.
By: Guionnet, Alice
Contributor(s): Ecole d'été de probabilités de Saint-Flour (36th : 2006)Material type: TextSeries: Lecture notes in mathematics (Springer-Verlag): 1957.Publisher: Berlin : Springer, ©2009Description: 1 online resource (xii, 294 pages) : illustrationsContent type: text Media type: computer Carrier type: online resourceISBN: 9783540698975; 3540698973; 1282127934; 9781282127937; 9783540698968; 3540698965Subject(s): Random matrices | Random matrices | Random matricesGenre/Form: Electronic books. Additional physical formats: Print version:: Large random matrices.DDC classification: 512.9434 LOC classification: QA3 | .L28 no.1957Other classification: O21-532 Online resources: Click here to access online
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Includes bibliographical references (pages 275-285) and index.
Print version record.
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.