Asymptotic Combinatorics with Application to Mathematical Physics

1. Front Matter

   Pages i-xv

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2. Matrix Models and Graph Enumeration

   1. Front Matter

      Pages 1-1

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   2. Matrix Quantum Mechanics

      • Vladimir Kazakov

      Pages 3-21

   3. Introduction to Matrix Models

      • E. Brézin

      Pages 23-50

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

      • V. Buslaev, L. Pastur

      Pages 51-70

   5. Combinatorics and Probability of Maps

      • V. A. Malyshev

      Pages 71-95

   6. The Combinatorics of Alternating Tangles: From Theory to Computerized Enumeration

      • J. L. Jacobsen, P. Zinn-Justin

      Pages 97-112

   7. Invariance Principles for Non-Uniform Random Mappings and Trees

      • David Aldous, Jim Pitman

      Pages 113-147

3. Integrable Models (Of Statistical Physics And Quantum Field Theory)

   1. Front Matter

      Pages 149-149

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   2. Renormalization Group Solution of Fermionic Dyson Model

      • M. D. Missarov

      Pages 151-166

   3. Statistical Mechanics and Number Theory

      • H. E. Boos, V. E. Korepin

      Pages 167-208

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

      • V. P. Maslov

      Pages 209-220

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

      • D. S. Grebenkov

      Pages 221-242

4. Representation Theory

   1. Front Matter

      Pages 243-243

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   2. Notes on Homogeneous Vector Bundles over Complex Flag Manifolds

      • Sergei Igonin

      Pages 245-254

   3. Representations Theory and Doubles of Yangians of Classical Lie Superalgebras

      • Vladimir Stukopin

      Pages 255-265

   4. Idempotent (Asymptotic) Mathematics and the Representation Theory

      • G. L. Litvinov, V. P. Maslov, G. B. Shpiz

      Pages 267-278

   5. A New Approach to Berezin Kernels and Canonical Representations

      • G. Van Dijk

      Pages 279-305

   6. Theta Hypergeometric Series

      • V. P. Spiridonov

      Pages 307-327

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.

• Combinatorics
• Eigenvalue
• Matrix
• Permutation
• Representation theory
• distribution
• mapping
• quantum mechanics
• vector bundle

• I.N.R.I.A., Le Chesnay, France

  Vadim Malyshev

• Steklov Mathematical Institute of Russian Academy of Sciences, St. Petersburg, Russia

  Anatoly Vershik

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