Applications of Random Matrices in Physics

J. P. Keating (auth.), Édouard Brézin, Vladimir Kazakov, Didina Serban, Paul Wiegmann, Anton Zabrodin (eds.)9781402045295, 1402045298, 1402045301, 140204531X, 9781402045301, 9781402045318

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.

---

Table of contents :
RANDOM MATRICES AND NUMBER THEORY….Pages 1-32
2D QUANTUM GRAVITY,MATRIX MODELS AND GRAPH COMBINATORICS….Pages 33-88
EIGENVALUE DYNAMICS, FOLLYTONS AND LARGEN LIMITS OF MATRICES….Pages 89-94
RANDOM MATRICES AND SUPERSYMMETRY IN DISORDERED SYSTEMS….Pages 95-137
HYDRODYNAMICS OF CORRELATED SYSTEMS….Pages 139-161
QCD, CHIRAL RANDOM MATRIX THEORYAND INTEGRABILITY….Pages 163-217
EUCLIDEAN RANDOMMATRICES:SOLVEDAND OPEN PROBLEMS….Pages 219-260
MATRIX MODELS AND GROWTH PROCESSES: FROM VISCOUS FLOWS TO THE QUANTUM HALL EFFECT….Pages 261-318
MATRIX MODELS AND TOPOLOGICAL STRINGS….Pages 319-378
MATRIX MODELS OF MODULI SPACE….Pages 379-401
MATRIX MODELS AND 2D STRING THEORY….Pages 403-457
MATRIX MODELS AS CONFORMALFIELD THEORIES….Pages 459-487
LARGE N ASYMPTOTICS OF ORTHOGONAL POLYNOMIALS FROM INTEGRABILITY TO ALGEBRAIC GEOMETRY….Pages 489-513