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Asymptotic Combinatorics with Application to Mathematical Physics

  • Book
  • © 2002

Overview

Editors:
  1. Vadim Malyshev

    1. I.N.R.I.A., Le Chesnay, France

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    You can also search for this editor in PubMed   Google Scholar

  2. Anatoly Vershik

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

    View editor publications

    You can also search for this editor in PubMed   Google Scholar

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 77)

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Table of contents (15 chapters)

  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
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Keywords

About this book

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.

Editors and Affiliations

  • 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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