Asymptotic Combinatorics with Applications to Mathematical Physics : A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001 / / edited by Anatoly M. Vershik

• Pubblicazione: Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2003
• Edizione: 1st ed. 2003.
• Descrizione fisica: 1 online resource (X, 250 p.)
• Disciplina: 510 s; 530.15/16
• Soggetto topico: Applied mathematics; Engineering mathematics; Physics; Combinatorial analysis; Group theory; Functional analysis; Differential equations, Partial; Applications of Mathematics; Physics, general; Combinatorics; Group Theory and Generalizations; Functional Analysis; Partial Differential Equations
• Persona (resp. second.): VershikAnatoly M
• Note generali: Bibliographic Level Mode of Issuance: Monograph
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: 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.
• Sommario/riassunto: 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.
• Titolo autorizzato: Asymptotic combinatorics with applications to mathematical physics
• ISBN: 3-540-44890-X
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 9910146272903321
• Lo trovi qui: Univ. Federico II
• Serie: Lecture Notes in Mathematics, . 0075-8434 ; ; 1815