## Asymptotic Combinatorics with Applications to Mathematical Physics: A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001, Issue 1815At 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. |

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Anal asymptotic representation theory automorphism Borodin branching graphs called caspidal central limit theorem characters classical coefficients combinatorial compute conjugacy class consider correlation functions correlation kernel corresponding Coxeter groups curves cycle decomposition defined Deift denote determinantal point processes dimensional distribution edge tree eigenvalues elements English translation ensemble equations example finite Fock space formula free cumulants free probability freeness genus GL(n group algebra harmonic analysis Hence infinite symmetric group integrable intersection theory isomorphic Kerov lectures Lemma length linear marked points Math Mathematics module moduli spaces multiplication normalized Okounkov Olshanski operator orthogonal polynomials permutation Petersburg Plancherel measure Poisson positive definite probability measure probability theory proof Proposition quantum random matrix theory random variables relation representation theory Riemann-Hilbert problem roots Russia spectral subgroup subset symmetric group tableau tion unique vector Vershik vertex vertices Voiculescu Young diagram Young graph z-measures