Applications of Random Matrices in Physics

1. Front Matter

   Pages I-X

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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

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.

• Baryon
• Chemistry
• Mathematics
• NATO
• Observable
• Physics
• Potential
• Science
• Series II
• correlation

• 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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