Title:
The Oxford handbook of random matrix theory / editors, Gernot Akemann, Jinho Baik, Philippe Di Francesco
Author:
Akemann, Gernot
Baik, Jinho, 1973-
Di Francesco, Philippe
Publication Information:
Oxford, U.K. ; New York : Oxford University Press, 2015
Call Number:
QA196.5 .O94 2015
Abstract:
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"
Edition:
Reprinted
ISBN:
9780198744191
Physical Description:
xxxi, 919 pages : illustrations ; 26 cm
General Note:
First published 2011. First published in paperback 2015.
Contents:
Introduction: -- Introduction and guide to the Handbook / History: an overview / Properties of Random Matrix Theory: -- Symmetry classes / Spectral statisitics of unitary emsembles / Spectral statistics of orthogonal and symplectic ensembles / Universality / Supersymmetry / Replica approach in random matrix theory / Painlevé transcendents / Random matrix theory and Integrable systems / Determinantal point processes / Random matrix representations of critical statistics / Heavy-tailed random matrices / Phase transitions / Two-matrix models and biorthogonal polynomials / Chain of matricies, loop equations and topological recursion / Unitary integrals and related matrix models / Non-Hermitian ensembles / Characteristic polynomials / Beta ensembles / Wigner matrices / Free probability theory / Random banded and sparse matrices / Applications of Random Matrix Theory: -- Number theory / Random permutations and related topics / Enumeration of maps / Knot theory and matrix integrals / Multivariate statistics / Algrebraic geometry and matrix models / Two-dimensional quantum gravity / String theory / Quantum chromodynamics / Quantum chaos and quantum graphs / Resonance scattering of waves in chaotic systems / Condensed matter physics / Classical and quantum optics / Extreme eigenvalues of Wishart matrices: application to entangled bipartite system / Random growth models / Random matrices and Laplacian growth / Financial applications of random matrix theory: a short review / Asymptotic singular value distributions in information theory / Random matrix theory and ribonucleic acid (RNA) folding / Complex networks
