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Applications of Random Matrices in Physics

  • Conference proceedings
  • © 2006

Overview

Editors:
  1. Édouard Brézin

    1. Laboratoire de Physique Théorique, Ecole Normale Supérieure, Paris, France

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  2. Vladimir Kazakov

    1. Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, Université Paris-VI, Paris, France

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  3. Didina Serban

    1. Service de Physique Théorique, CEA Saclay, Gif-sur-Yvette Cedex, France

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  4. Paul Wiegmann

    1. James Frank Institute, University of Chicago, Chicago, U.S.A.

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  5. Anton Zabrodin

    1. Institute of Biochemical Physics, Moscow, Russia
      ITEP, Moscow, Russia

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  • collection of lectures of well known specialists in random matrices and their applications
  • broad coverage of various physical and mathematical subjects unified by common methods related to random matrices
  • series of lectures with systematic covering of particular topics, from basics to the modern state and research projects

Part of the book series: NATO Science Series II: Mathematics, Physics and Chemistry (NAII, volume 221)

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Table of contents (13 papers)

  1. Front Matter

    Pages I-X
    Download chapter PDF

  2. RANDOM MATRICES AND NUMBER THEORY

    • J. P. Keating
    Pages 1-32

  3. 2D QUANTUM GRAVITY,MATRIX MODELS AND GRAPH COMBINATORICS

    • P. Di Francesco
    Pages 33-88

  4. EIGENVALUE DYNAMICS, FOLLYTONS AND LARGEN LIMITS OF MATRICES

    • Joakim Arnlind, Jens Hoppe
    Pages 89-94

  5. RANDOM MATRICES AND SUPERSYMMETRY IN DISORDERED SYSTEMS

    • K.B. Efetov
    Pages 95-137

  6. HYDRODYNAMICS OF CORRELATED SYSTEMS

    • Alexander G. Abanov
    Pages 139-161

  7. QCD, CHIRAL RANDOM MATRIX THEORYAND INTEGRABILITY

    • J.J.M. Verbaarschot
    Pages 163-217

  8. EUCLIDEAN RANDOMMATRICES:SOLVEDAND OPEN PROBLEMS

    • Giorgio Parisi
    Pages 219-260

  9. MATRIX MODELS AND GROWTH PROCESSES: FROM VISCOUS FLOWS TO THE QUANTUM HALL EFFECT

    • A. Zabrodin
    Pages 261-318

  10. MATRIX MODELS AND TOPOLOGICAL STRINGS

    • Marcos Mariño
    Pages 319-378

  11. MATRIX MODELS OF MODULI SPACE

    • Sunil Mukhi
    Pages 379-401

  12. MATRIX MODELS AND 2D STRING THEORY

    • Emil J. Martinec
    Pages 403-457

  13. MATRIX MODELS AS CONFORMALFIELD THEORIES

    • Ivan K. Kostov
    Pages 459-487

  14. LARGE N ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS FROM INTEGRABILITY TO ALGEBRAIC GEOMETRY

    • B. Eynard
    Pages 489-513
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Keywords

About this book

Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.

Editors and Affiliations

  • Laboratoire de Physique Théorique, Ecole Normale Supérieure, Paris, France

    Édouard Brézin

  • Laboratoire de Physique Théorique de l’Ecole Normale Supérieure, Université Paris-VI, Paris, France

    Vladimir Kazakov

  • Service de Physique Théorique, CEA Saclay, Gif-sur-Yvette Cedex, France

    Didina Serban

  • James Frank Institute, University of Chicago, Chicago, U.S.A.

    Paul Wiegmann

  • Institute of Biochemical Physics, Moscow, Russia

    Anton Zabrodin

  • ITEP, Moscow, Russia

    Anton Zabrodin

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