04790nam 22007695 450 99646648250331620200629172542.03-540-69897-310.1007/978-3-540-69897-5(CKB)1000000000718095(DE-He213)978-3-540-69897-5(SSID)ssj0000318616(PQKBManifestationID)11239942(PQKBTitleCode)TC0000318616(PQKBWorkID)10310827(PQKB)10037290(MiAaPQ)EBC3064144(PPN)134129989(EXLCZ)99100000000071809520100301d2009 u| 0engurnn|008mamaatxtrdacontentcrdamediacrrdacarrierLarge Random Matrices: Lectures on Macroscopic Asymptotics[electronic resource] École d'Été de Probabilités de Saint-Flour XXXVI – 2006 /by Alice Guionnet1st ed. 2009.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2009.1 online resource (XII, 294 p. 13 illus.) École d'Été de Probabilités de Saint-Flour,0721-5363 ;1957Bibliographic Level Mode of Issuance: Monograph3-540-69896-5 Includes bibliographical references and index.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.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.École d'Été de Probabilités de Saint-Flour,0721-5363 ;1957Discrete mathematicsProbabilitiesAlgebraMatrix theoryFunctional analysisCombinatoricsDiscrete Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M29000Probability Theory and Stochastic Processeshttps://scigraph.springernature.com/ontologies/product-market-codes/M27004Algebrahttps://scigraph.springernature.com/ontologies/product-market-codes/M11000Linear and Multilinear Algebras, Matrix Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M11094Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Discrete mathematics.Probabilities.Algebra.Matrix theory.Functional analysis.Combinatorics.Discrete Mathematics.Probability Theory and Stochastic Processes.Algebra.Linear and Multilinear Algebras, Matrix Theory.Functional Analysis.Combinatorics.512.9434Guionnet Aliceauthttp://id.loc.gov/vocabulary/relators/aut472372Ecole d'été de probabilités de Saint-Flour(36th :2006)BOOK996466482503316Large random matrices230205UNISA