Asymptotic Combinatorics With Application to

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.

Preface

vii

Program

ix

List of participants

xiii

PART ONE / MATRIX MODELS AND GRAPH ENUMERATION

Matrix Quantum Mechanics

3

(20)

V. Kazakov

Introduction to matrix models

23

(28)

E. Brezin

A Class of the Multi-Interval Eigenvalue Distributions of Matrix Models and Related Structures

51

(20)

V. Buslaev

L. Pastur

Combinatories and Probability of Maps

71

(26)

V. A. Malyshev

The Combinatorics of Alternating Tangles: from theory to computerized enumerations

97

(16)

J. L. Jacobsen

P. Zinn-Justin

Invariance Principles for Non-uniform Random Mappings and Trees

113

(38)

D. Aldous

J. Pitman

PART TWO / INTEGRABLE MODELS (OF STATISTICAL PHYSICS AND QUANTUM FIELD THEORY)

Renormalization group solution of fermionic Dyson model

151

(16)

M. D. Missarov

Statistical Mechanics and Number Theory

167

(42)

H. E. Boos

V. E. Korepin

Quantization of Thermodynamics and the Bardeen-Cooper-Schriffer-Bogolyubov Equation

209

(12)

V. P. Maslov

Approximate Distribution of Hitting Probabilities for a Regular Surface with Compact Support in 2D

221

(24)

S. Grebenkov

PART THREE / REPRESENTATION THEORY

Notes on homogeneous vector bundles over complex flag manifolds

245

(10)

S. Igonin

Representations Theory and Doubles of Yangians of Classical Lie Superalgebras

255

(12)

V. Stukopin

Idempotent (asymptotic) Mathematics and the Representation theory

267

(12)

G. L. Litvinov

V. P. Maslov

G. B. Shpiz

A new approach to Berezin kernels canonical representations

279

(28)

G. van Dijk

Theta Hypergeometric Series

307

V. P. Spiridonov

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Asymptotic Combinatorics With Application to Mathematical Physics

Summary

Table of Contents

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Asymptotic Combinatorics With Application to Mathematical Physics

Summary

Table of Contents

Supplemental Materials

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