04697nam 22008295 450 99646652780331620200630073829.03-540-44890-X10.1007/3-540-44890-X(CKB)1000000000437263(SSID)ssj0000321456(PQKBManifestationID)11283929(PQKBTitleCode)TC0000321456(PQKBWorkID)10279514(PQKB)10093682(DE-He213)978-3-540-44890-7(MiAaPQ)EBC3071644(PPN)155195026(EXLCZ)99100000000043726320121227d2003 u| 0engurnn|008mamaatxtccrAsymptotic Combinatorics with Applications to Mathematical Physics[electronic resource] A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001 /edited by Anatoly M. Vershik1st ed. 2003.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2003.1 online resource (X, 250 p.) Lecture Notes in Mathematics,0075-8434 ;1815Bibliographic Level Mode of Issuance: Monograph3-540-40312-4 Includes bibliographical references.Random matrices, orthogonal polynomials and Riemann — Hilbert problem -- Asymptotic representation theory and Riemann — Hilbert problem -- Four Lectures on Random Matrix Theory -- Free Probability Theory and Random Matrices -- Algebraic geometry,symmetric functions and harmonic analysis -- A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group -- Random trees and moduli of curves -- An introduction to harmonic analysis on the infinite symmetric group -- Two lectures on the asymptotic representation theory and statistics of Young diagrams -- III Combinatorics and representation theory -- Characters of symmetric groups and free cumulants -- Algebraic length and Poincaré series on reflection groups with applications to representations theory -- Mixed hook-length formula for degenerate a fine Hecke algebras.At the Summer School Saint Petersburg 2001, the main lecture courses bore on recent progress in asymptotic representation theory: those written up for this volume deal with the theory of representations of infinite symmetric groups, and groups of infinite matrices over finite fields; Riemann-Hilbert problem techniques applied to the study of spectra of random matrices and asymptotics of Young diagrams with Plancherel measure; the corresponding central limit theorems; the combinatorics of modular curves and random trees with application to QFT; free probability and random matrices, and Hecke algebras.Lecture Notes in Mathematics,0075-8434 ;1815Applied mathematicsEngineering mathematicsPhysicsCombinatoricsGroup theoryFunctional analysisPartial differential equationsApplications of Mathematicshttps://scigraph.springernature.com/ontologies/product-market-codes/M13003Physics, generalhttps://scigraph.springernature.com/ontologies/product-market-codes/P00002Combinatoricshttps://scigraph.springernature.com/ontologies/product-market-codes/M29010Group Theory and Generalizationshttps://scigraph.springernature.com/ontologies/product-market-codes/M11078Functional Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M12066Partial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Applied mathematics.Engineering mathematics.Physics.Combinatorics.Group theory.Functional analysis.Partial differential equations.Applications of Mathematics.Physics, general.Combinatorics.Group Theory and Generalizations.Functional Analysis.Partial Differential Equations.510 s530.15/16Vershik Anatoly Medthttp://id.loc.gov/vocabulary/relators/edtMiAaPQMiAaPQMiAaPQBOOK996466527803316Asymptotic combinatorics with applications to mathematical physics145973UNISA