Asymptotic Combinatorics with Applications to Mathematical Physics
A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
Published on 20. June 2003
Book
Paperback/Softback
X, 250 pages
978-3-540-40312-8 (ISBN)
Description
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.
More details
Series
Edition
2003 ed.
Language
English
Place of publication
Berlin
Germany
Publishing group
Springer Berlin
Target group
Professional and scholarly
Research
Illustrations
X, 250 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 15 mm
Weight
400 gr
ISBN-13
978-3-540-40312-8 (9783540403128)
DOI
10.1007/3-540-44890-X
Schweitzer Classification
Other editions
Additional editions
Anatoly M. Vershik
Asymptotic Combinatorics with Applications to Mathematical Physics
A European Mathematical Summer School held at the Euler Institute, St. Petersburg, Russia, July 9-20, 2001
E-Book
07/2003
Springer
€53.49
Available for download
Content
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.