Random Matrices

by Madan L Mehta

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.
APresentation of many new results in one place for the first time.
AFirst time coverage of skew-orthogonal and bi-orthogonal polynomials and their use in the evaluation of some multiple integrals.
AFredholm determinants and Painlev(r) equations.
AThe three Gaussian ensembles (unitary, orthogonal, and symplectic); their n-point correlations, spacing probabilities.
AFredholm determinants and inverse scattering theory.
AProbability densities of random determinants."

708 pages, Kindle Edition

First published November 2, 2004

Reviews

[Chaher Chouikhi · Rating 5 out of 5]

I need this amazing book to finish my studies. I would recommand it to my class.