Asymptotic combinatorics with applications to mathematical physics : a European mathematical summer school held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001 00

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. Introduction -- Part I: Random Matrices, Orthogonal Polynomials And Riemann-hilbert Problem: A. Borodin: Asymptotic Representation Theory And Riemann-hilbert Problem; P. Deift: Four Lectures On Random Matrix Theory; R. Speicher: Free Probability Theory And Random Matrices -- Part Ii: Algebraic Geometry, Symmetric Functions And Harmonic Analysis: A. Hora: A Noncommutative Version Of Kerov's Gaussian Limit For The Plancherel Measure Of The Symmetric Group; A. Okounkov: Random Tress And Moduli Of Curves; G. Olshanski: An Introduction To Harmonic Analysis On The Infinite Symmetric Group; A. Vershik: Two Lectures On The Asymptotic Representation Theory And Statistics Of Young Diagrams -- Part Iii: Combinatorics And Representation Theory: P. Biane: Characters Of Symmetric Groups And Free Cumulants; M. Bozejko And R. Szwarc: Algebraic Length And Poincaré Series On Reflection Groups With Applications To Representation Theory; M. Nazarov: Mixed Hook-length Formula For Degenerate Affine Hecke Algebras; Addendum: Information About The School. Anatoly M. Vershik (ed.). Includes Bibliographical References. Asymptotic representation theory and Riemann — Hilbert problem....Pages 3-19 Four Lectures on Random Matrix Theory....Pages 21-52 Free Probability Theory and Random Matrices....Pages 53-73 A Noncommutative Version of Kerov’s Gaussian Limit for the Plancherel Measure of the Symmetric Group....Pages 77-88 Random trees and moduli of curves....Pages 89-126 An introduction to harmonic analysis on the infinite symmetric group....Pages 127-160 Two lectures on the asymptotic representation theory and statistics of Young diagrams....Pages 161-182 Characters of symmetric groups and free cumulants....Pages 185-200 Algebraic length and Poincaré series on reflection groups with applications to representations theory....Pages 201-221 Mixed hook-length formula for degenerate a fine Hecke algebras....Pages 223-236