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Advanced topics in random matrices

Author: Florent Benaych-GeorgesCharles BordenaveMireille CapitaineCatherine Donati-MartinAntti KnowlesAll authors
Publisher: Paris : Société mathématique de France, 2017. ©2017
Series: Panoramas et synthèses, 53.
Edition/Format:   Print book : FrenchView all editions and formats
Summary:
This book provides three accessible panoramas and syntheses on advanced topics in random matrix theory: (1) local semicircle law for Wigner matrices and applications to eigenvectors delocalization, rigidity of eigenvalues, and fourth moment theorem; (2) spectrum of random graphs, recent advances on eigenvalues and eigenvectors, and open problems; and (3) deformed random matrices and free probability, unified  Read more...
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Document Type: Book
All Authors / Contributors: Florent Benaych-Georges; Charles Bordenave; Mireille Capitaine; Catherine Donati-Martin; Antti Knowles; Djalil Chafaï; S Péché; Béatrice de Tilière
ISBN: 9782856298503 2856298508
OCLC Number: 1035409692
Notes: "These three chapters take their roots in the conference États de la Recherche en Matrices Aléatoires, held during the period December 1-4, 2014, in Institut Henri Poincaré, Paris."- foreword
Description: ix, 190 pages ; 24 cm.
Contents: Local semicircle law for Wigner matrices --
Spectrum of random graphs --
Spectrum of deformed random matrices and free probability.
Series Title: Panoramas et synthèses, 53.
Responsibility: Florent Benaych-Georges, Charles Bordenave, Mireille Capitaine, Catherine Donati-Martin, Antti Knowles ; edited by F. Benaych-Georges, D. Chafaï, S. Péché, B. de Tilière.

Abstract:

This book provides three accessible panoramas and syntheses on advanced topics in random matrix theory: (1) local semicircle law for Wigner matrices and applications to eigenvectors delocalization, rigidity of eigenvalues, and fourth moment theorem; (2) spectrum of random graphs, recent advances on eigenvalues and eigenvectors, and open problems; and (3) deformed random matrices and free probability, unified understanding of various asymptotic phenomena, such as spectral measure description, localization and fluctuations of extremal eigenvalues, and eigenvectors behavior.

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