LEADER 03534nam 2200565Ia 450 001 9910483914503321 005 20200520144314.0 010 $a3-540-69897-3 024 7 $a10.1007/978-3-540-69897-5 035 $a(CKB)1000000000718095 035 $a(DE-He213)978-3-540-69897-5 035 $a(SSID)ssj0000318616 035 $a(PQKBManifestationID)11239942 035 $a(PQKBTitleCode)TC0000318616 035 $a(PQKBWorkID)10310827 035 $a(PQKB)10037290 035 $a(MiAaPQ)EBC3064144 035 $a(PPN)134129989 035 $a(EXLCZ)991000000000718095 100 $a20081208d2009 uy 0 101 0 $aeng 135 $aurnn|008mamaa 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aLarge random matrices $electures on macroscopic asymptotics : Ecole d'Ete des Probabilites de Saint-Flour XXXVI - 2006 /$fAlice Guionnet 205 $a1st ed. 2009. 210 $aBerlin ;$aLondon $cSpringer$d2009 215 $a1 online resource (XII, 294 p. 13 illus.) 225 1 $aLecture notes in mathematics (Springer-Verlag) ;$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 $aRandom matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the asymptotic distribution of matrices, which is naturally defined in the context of free probability and operator algebra. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Maury Bramson and Steffen Lauritzen. 410 0$aLecture notes in mathematics (Springer-Verlag) ;$v1957. 606 $aRandom matrices$vCongresses 606 $aAsymptotic expansions$vCongresses 615 0$aRandom matrices 615 0$aAsymptotic expansions 676 $a512.9434 701 $aGuionnet$b Alice$0472372 712 12$aEcole d'e?te? de probabilite?s de Saint-Flour$d(36th :$f2006) 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910483914503321 996 $aLarge random matrices$9230205 997 $aUNINA