Philippe Di Francesco - Böcker

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of

With a foreword by Freeman Dyson, the handbook brings together leading mathematicians and physicists to offer a comprehensive overview of random matrix theory, including a guide to new developments and the diverse range of applications of this approach.In part one, all modern and classical techniques of solving random matrix models are explored, including orthogonal polynomials, exact replicas or supersymmetry. Further, all main extensions of the classical Gaussian ensembles of Wigner and Dyson are introduced including sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered, in disciplines ranging from physics and mathematics to biology and engineering. This includes standard fields such as number theory, quantum chaos or quantum chromodynamics, as well as recent developments such as partitions, growth models, knot theory, wireless communication or bio-polymer folding. The handbook is suitable both for introducing novices to this area of research and as a main source of reference for active researchers in mathematics, physics and engineering.

As recent developments have shown, supersymmetric quantum field theory and string theory are intimately related, with advances in one area often shedding light on the other. The topics covered in the present volume include duality in field theory, in particular in supersymmetric field theory and supergravity, and in string theory. The Seiberg-Witten theory and its recent developments are also covered in detail. A large fraction of the volume is devoted to the current state of the art in M-theory, in particular its underlying superalgebra as well as its connection with superstring and N = 2 strings. The physics of D-branes and its essential role in the computation of the black hole entropy is also carefully covered. Finally, the last two sets of lectures are devoted to the matrix approach to non-perturbative string theory.