Asymptotic Combinatorics with Application to Mathematical Physics [Paperback]

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.Proceedings of the NATO Advanced Study Institute, held in St.Petersburg, Russia, 9-22 July 2001New 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.Preface. Program. List of participants. Part One: Matrix Models and Graph Enumeration. Matrix Quantum Mechanics; V. Kazakov. Introduction to matrix models; E. Br?zin. A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures; V. Buslaev, L. Pastur. Combinatorics and Probability of Maps; V.A. Malyshev. The Combinatorics of Alternating Tangles: from theory to computerized enumeration; J.L. Jacobsen, P. Zinn-Justin. Invariance Principles for Non-uniform Random Mappings and Trees; D. Aldous, J. Pitman. Part Two: Integrable Models (of Statistical Physics and Quantum Field Theory). Renormalization group solution of fermionic Dyson model; M.D. Missarov. Statistical Mechanics and Number Theory; H.E. Boos, V.E. Korepin. Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation; V.P. Maslov. Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D; D.S. Grebenkov. Part Three: Representation Theory. Notes on homogeneous vector bundles over complex flag manifolds; S. Igonin. Representation Theory and Doubles ol³