Asymptotic combinatorics with applications to mathematical physics : a European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
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書誌事項
Asymptotic combinatorics with applications to mathematical physics : a European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
（Lecture notes in mathematics, 1815 . European Mathematical Society）
Springer, c2003
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注記
Includes bibliographical references
内容説明・目次
内容説明
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.
目次
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 Poincare series on reflection groups with applications to representations theory.- Mixed hook-length formula for degenerate a fine Hecke algebras.
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