Asymptotic Combinatorics with Applications to Mathematical Physics: A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001Anatoly M. Vershik 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. |
Contents
| 3 | |
Four Lectures on Random Matrix Theory | 20 |
P Deift 21 | 53 |
Algebraic geometry symmetric functions and harmonic | 77 |
An introduction to harmonic analysis on the infinite | 127 |
Two lectures on the asymptotic representation theory | 161 |
Characters of symmetric groups and free cumulants | 185 |
Algebraic length and Poincaré series on reflection groups | 201 |
Mixed hooklength formula for degenerate affine Hecke | 222 |
Addendum Information about the school | 237 |
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Asymptotic Combinatorics with Applications to Mathematical Physics Anatoly M. Vershik No preview available - 2014 |
Common terms and phrases
asymptotics automorphism Borodin branching graphs called characters coefficients combinatorial compute conjugacy class consider convergence correlation functions correlation kernel corresponding curves decomposition defined Deift denote determinantal point processes distribution edge labels edge tree eigenvalues elements English translation ensemble equations example finite Fock space formula free cumulants free probability freeness genus g GL(n group algebra harmonic analysis hence homotopy type Hurwitz problem infinite symmetric group intersection theory irreducible isomorphic Kerov lectures Lemma linear marked points Math Mathematics Mg,n moduli spaces multiplication NC(n non-crossing partitions nontrivial Okounkov Olshanski Orthogonal polynomials permutations Plancherel measure Poisson positive definite probability measure probability theory proof Proposition random matrix theory random variables relation representation theory Riemann–Hilbert problem spectral spherical representations subset symmetric group tableau unique vector Vershik vertex vertices Voiculescu Young diagram Young graph