Random Matrices: Revised and Enlarged Second Edition (ISSN)

This book presents a coherent and detailed analytical treatment of random matrices, leading in particular to the calculation of n-point correlations, of spacing probabilities, and of a number of statistical quantities. The results are used in describing the statistical properties of nuclear excitations, the energies of chaotic systems, the ultrasonic frequencies of structural materials, the zeros of the Riemann zeta function, and in general the characteristic energies of any sufficiently complicated system.
Since the publication of Random Matrices (Academic Press, 1967) so many new results have emerged both in theory and in applications, that this edition is almost completely revised to reflect the developments. For example, the theory of matrices with quaternion elements was developed to compute certain multiple integrals, and the inverse scattering theory was used to derive asymptotic results. The discovery of Selberg's 1944 paper devoted to a famous multiple integral.
This book is of special interest to physicists and mathematicians. It is self-contained and therefore can also be used by students and practitioners in other disciplines who have a knowledge of undergraduate level mathematics.

Audience: Physicists, mathematicians, and any scientist working in the fields of nuclear physics, solid state (especially amorphous material), chaotic systems, hydrodynamics, structural acoustics, multiple integrals, orthogonal polynomials, applied mathematical methods, zeta functions, and Dirichlet series. Prerequisite: Undergraduate mathematics, although subjects are treated at an advanced level.