Asymptotic Combinatorics with Application to Mathematical Physics

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V.A. Malyshev, A.M. Vershik
Springer Science & Business Media, Aug 31, 2002 - Science - 327 pages
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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.
 

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Contents

MATRIX QUANTUM MECHANICS
3
INTRODUCTION TO MATRIX MODELS
23
A CLASS OF THE MULTIINTERVAL EIGENVALUE DISTRIBUTIONS OF MATRIX MODELS AND RELATED STRUCTURES
51
COMBINATORICS AND PROBABILITY OF MAPS
71
THE COMBINATORICS OF ALTERNATING TANGLES FROM THEORY TO COMPUTERIZED ENUMERATION
97
INVARIANCE PRINCIPLES FOR NONUNIFORM RANDOM MAPPINGS AND TREES
113
INTEGRABLE MODELS OF STATISTICAL PHYSICS AND QUANTUM FIELD THEORY
149
RENORMALIZATION GROUP SOLUTION OF FERMIONIC DYSON MODEL
151
QUANTIZATION OF THERMODYNAMICS AND THE BARDEENCOOPERSCHRIFFERBOGOLYUBOV EQUATION
209
APPROXIMATE DISTRIBUTION OF HITTING PROBABILITIES FOR A REGULAR SURFACE WITH COMPACT SUPPORT IN 2D
221
REPRESENTATION THEORY
243
NOTES ON HOMOGENEOUS VECTOR BUNDLES OVER COMPLEX FLAG MANIFOLDS
245
REPRESENTATIONS THEORY AND DOUBLES OF YANGIANS OF CLASSICAL LIE SUPERALGEBRAS
255
IDEMPOTENT ASYMPTOTIC MATHEMATICS AND THE REPRESENTATION THEORY
267
A NEW APPROACH TO BEREZIN KERNELS AND CANONICAL REPRESENTATIONS
279
THETA HYPERGEOMETRIC SERIES
307

STATISTICAL MECHANICS AND NUMBER THEORY
167

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