Asymptotic Combinatorics with Application to Mathematical Physics

by V.A. Malyshev (Editor), A.M. Vershik (Editor)

Overview

New and striking results obtained in recent years from an intensive study of asymptotic combinatorics have led to a new, higher level of understanding of related problems: the theory of integrable systems, the Riemann-Hilbert problem, asymptotic representation theory, spectra of random matrices, combinatorics of Young diagrams and permutations, and even some aspects of quantum field theory.

Product Details

ISBN-13:	9781402007934
Publisher:	Springer Netherlands
Publication date:	08/31/2002
Series:	NATO Science Series II: Mathematics, Physics and Chemistry , #77
Edition description:	Softcover reprint of the original 1st ed. 2002
Pages:	327
Product dimensions:	6.30(w) x 9.45(h) x (d)

Table of Contents

One / Matrix Models and Graph Enumeration.- Matrix Quantum Mechanics.- to matrix models.- A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures.- Combinatorics and Probability of Maps.- The Combinatorics of Alternating Tangles: from theory to computerized enumeration.- Invariance Principles for Non-uniform Random Mappings and Trees.- Two / Integrable Models (of Statistical Physics and Quantum Field Theory).- Renormalization group solution of fermionic Dyson model.- Statistical Mechanics and Number Theory.- Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation.- Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D.- Three / Representation Theory.- Notes on homogeneous vector bundles over complex flag manifolds.- Representations Theory and Doubles of Yangians of Classical Lie Superalgebras.- Idempotent (asymptotic) Mathematics and the Representation theory.- A new approach to Berezin kernels and canonical representations.- Theta Hypergeometric Series.