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Full Description
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.
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.
