## 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.

Material type: TextSeries: Lecture Notes in Mathematics ; 1815Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg, 2003Description: X, 250 p. online resourceContent type: text Media type: computer Carrier type: online resourceISBN: 9783540448907Subject(s): Mathematics | Group theory | Functional analysis | Differential equations, partial | Combinatorics | Distribution (Probability theory) | Mathematics | Combinatorics | Group Theory and Generalizations | Functional Analysis | Partial Differential Equations | Probability Theory and Stochastic ProcessesAdditional physical formats: Printed edition:: No titleDDC classification: 511.6 LOC classification: QA164-167.2Online resources: Click here to access onlineCurrent library | Home library | Call number | Materials specified | URL | Status | Date due | Barcode |
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IMSc Library | IMSc Library | Link to resource | Available | EBK1289 |

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.

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.

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