The Oxford Handbook Of Random Matrix Theory

With a foreword by Freeman Dyson, the Oxford Handbook of Random Matrix Theory 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 the first part of this book, 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 for example sparse, heavy tailed, non-Hermitian or multi-matrix models. In the second and larger part, all major applications are covered 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