Random Matrices, Volume 142, Third Edition (Pure and Applied Mathematics) - Softcover

Lal Mehta, Madan

Softcover

ISBN 10: 1483299899 ISBN 13: 9781483299891

Publisher: Academic Press, 2004

Synopsis

This book gives a coherent and detailed description of analytical methods devised to study random matrices. These methods are critical to the understanding of various fields in in mathematics and mathematical physics, such as nuclear excitations, ultrasonic resonances of structural materials, chaotic systems, the zeros of the Riemann and other zeta functions. More generally they apply to the characteristic energies of any sufficiently complicated system and which have found, since the publication of the second edition, many new applications in active research areas such as quantum gravity, traffic and communications networks or stock movement in the financial markets.

This revised and enlarged third edition reflects the latest developements in the field and convey a greater experience with results previously formulated. For example, the theory of skew-orthogoanl and bi-orthogonal polynomials, parallel to that of the widely known and used orthogonal polynomials, is explained here for the first time.

· Presentation of many new results in one place for the first time.
· First time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals.
· Fredholm determinants and Painlevé equations.
· The three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.
· Fredholm determinants and inverse scattering theory.
· Probability densities of random determinants.

About this title

Book Description

Gives a coherent and detailed description of analytical methods devised to study random matrices.

Edition details

• Publisher: Academic Press
• Publication date: 2004
• ISBN 10: 1483299899
• ISBN 13: 9781483299891
• Binding: Paperback
• Language: English
• Edition number: 3
• Number of pages: 706