Asymptotic Combinatorics with Applications to Mathematical Physics: A European Mathematical Summer School held at the Euler Institute, St. Petersburg, . 2001 (Lecture Notes in Mathematics, 1815)

ISBN 10: 3540403124 / ISBN 13: 9783540403128

Editore: Springer, 2003

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Dati bibliografici

• Titolo: Asymptotic Combinatorics with Applications to Mathematical Physics: A European Mathematical Summer School held at the Euler Institute, St. Petersburg, . 2001 (Lecture Notes in Mathematics, 1815)
• Editore: Springer
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 3540403124
• ISBN 13: 9783540403128
• Rilegatura: Brossura
• Condizione: New

Descrizione articolo

Riassunto

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.

Contenuti

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.