Title	Asymptotic 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. Vershik, Yuri Yakubovich
Imprint	Berlin, Heidelberg : Springer Berlin Heidelberg, 2003
Connect to	http://dx.doi.org/10.1007/3-540-44890-X
Descript	X, 250 p. online resource

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

Random matrices, orthogonal polynomials and Riemann โ{128}{148} Hilbert problem -- Asymptotic representation theory and Riemann โ{128}{148} 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 Kerovโ{128}{153}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 Poincarรฉ series on reflection groups with applications to representations theory -- Mixed hook-length formula for degenerate a fine Hecke algebras