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101 0 $aeng
135   $aurnn|008mamaa
181   $ctxt$2rdacontent
182   $cc$2rdamedia
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200 10$aLarge Random Matrices: Lectures on Macroscopic Asymptotics$b[electronic resource] $eÉcole d'Été de Probabilités de Saint-Flour XXXVI ? 2006 /$fby Alice Guionnet
205   $a1st ed. 2009.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2009.
215   $a1 online resource (XII, 294 p. 13 illus.) 
225 1 $aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v1957
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-69896-5 
320   $aIncludes bibliographical references and index.
327   $aWigner 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.
330   $aRandom matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the asymptotic distribution of matrices, which is naturally defined in the context of free probability and operator algebra. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Maury Bramson and Steffen Lauritzen.
410  0$aÉcole d'Été de Probabilités de Saint-Flour,$x0721-5363 ;$v1957
606   $aDiscrete mathematics
606   $aProbabilities
606   $aAlgebra
606   $aMatrix theory
606   $aFunctional analysis
606   $aCombinatorics
606   $aDiscrete Mathematics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29000
606   $aProbability Theory and Stochastic Processes$3https://scigraph.springernature.com/ontologies/product-market-codes/M27004
606   $aAlgebra$3https://scigraph.springernature.com/ontologies/product-market-codes/M11000
606   $aLinear and Multilinear Algebras, Matrix Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11094
606   $aFunctional Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M12066
606   $aCombinatorics$3https://scigraph.springernature.com/ontologies/product-market-codes/M29010
615  0$aDiscrete mathematics.
615  0$aProbabilities.
615  0$aAlgebra.
615  0$aMatrix theory.
615  0$aFunctional analysis.
615  0$aCombinatorics.
615 14$aDiscrete Mathematics.
615 24$aProbability Theory and Stochastic Processes.
615 24$aAlgebra.
615 24$aLinear and Multilinear Algebras, Matrix Theory.
615 24$aFunctional Analysis.
615 24$aCombinatorics.
676   $a512.9434
700   $aGuionnet$b Alice$4aut$4http://id.loc.gov/vocabulary/relators/aut$0472372
712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(36th :$f2006)
906   $aBOOK
912   $a996466482503316
996   $aLarge random matrices$9230205
997   $aUNISA