Asymptotic Combinatorics with Applications to Mathematical Physics (eBook, PDF)

A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
Redaktion: Vershik, Anatoly M.

• Format: PDF

Produktbeschreibung

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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Produktdetails

• Verlag: Springer Berlin Heidelberg
• Seitenzahl: 250
• Erscheinungstermin: 3. Juli 2003
• Englisch
• ISBN-13: 9783540448907
• Artikelnr.: 53102362

Autorenporträt

Anatoly M. Vershik, Russian Academy of Sciences, St. Petersburg, Russia

Inhaltsangabe

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.