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The Oxford Handbook of Random Matrix Theory

Online ISBN:
9780191873997
Print ISBN:
9780198744191
Publisher:
Oxford University Press
Book

The Oxford Handbook of Random Matrix Theory

Gernot Akemann (ed.),
Gernot Akemann
(ed.)
Universität Bielefeld
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Gernot Akemann, Fakultät für Physik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany, akemann@physik.uni-bielefeld.de

Jinho Baik (ed.),
Jinho Baik
(ed.)
University of Michigan
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Jinho Baik, 530 Church Street, Department of Mathematics, University of Michigan, Ann Arbor, MI 48109-1043, USA, baik@umich.edu

Philippe Di Francesco (ed.)
Philippe Di Francesco
(ed.)
Institut de Physique Théorique
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Philippe Di Francesco, Institut de Physique Théorique, CEA/Saclay, Orme des Merisiers, F-91191 Gif-sur-Yvette Cedex, France, philippe.di-francesco@cea.fr

Published online:
8 August 2018
Published in print:
17 September 2015
Online ISBN:
9780191873997
Print ISBN:
9780198744191
Publisher:
Oxford University Press

Abstract

This handbook showcases the major aspects and modern applications of random matrix theory (RMT). It examines the mathematical properties and applications of random matrices and some of the reasons why RMT has been very successful and continues to enjoy great interest among physicists, mathematicians and other scientists. It also discusses methods of solving RMT, basic properties and fundamental objects in RMT, and different models and symmetry classes in RMT. Topics include the use of classical orthogonal polynomials (OP) and skew-OP to solve exactly RMT ensembles with unitary, and orthogonal or symplectic invariance respectively, all at finite matrix size; the supersymmetric and replica methods; determinantal point processes; Painlevé transcendents; the fundamental property of RMT known as universality; RNA folding; two-dimensional quantum gravity; string theory; and the mathematical concept of free random variables. In addition to applications to mathematics and physics, the book considers broader applications to other sciences, including economics, engineering, biology, and complex networks.

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