Asymptotic Combinatorics with Applications to Mathematical Physics - A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001

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.

List of contents

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.

Product details

• Assisted by: Anatoly M. Vershik (Editor)
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 20.06.2003
• EAN: 9783540403128
• ISBN: 978-3-540-40312-8
• No. of pages: 250
• Weight: 420 g
• Illustrations: X, 250 p.
• Series: Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; B, Differentialrechnung und -gleichungen, Funktionalanalysis und Abwandlungen, Group Theory, Combinatorics, Physics, Mathematics and Statistics, Applications of Mathematics, Functional Analysis, Discrete Mathematics, Physics and Astronomy, Physics, general, Combinatorics & graph theory, Partial Differential Equations, Differential calculus & equations, Differential equations, Groups & group theory, Group Theory and Generalizations, Engineering mathematics, Applied mathematics, Functional analysis & transforms