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Random Matrices, Second Edition: Revised and Enlarged Second Edition (Pure and Applied Mathematics), by Madan Lal Mehta
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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 on a multiple integral also gave rise to hundreds of recent publications.
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. Of special interest to physicists and mathematicians, the book is self-contained and the reader need know mathematics only at the undergraduate level.
Key Features
* The three Gaussian ensembles, unitary, orthogonal, and symplectic; their n-point correlations and spacing probabilities
* The three circular ensembles: unitary, orthogonal, and symplectic; their equivalence to the Gaussian
* Matrices with quaternion elements
* Integration over alternate and mixed variables
* Fredholm determinants and inverse scattering theory
* A Brownian motion model of the matrices
* Computation of the mean and of the variance of a number of statistical quantities
* Selberg's integral and its consequences
- Sales Rank: #6005116 in Books
- Published on: 1990-12-12
- Original language: English
- Number of items: 1
- Dimensions: 1.34" h x 6.29" w x 9.32" l,
- Binding: Hardcover
- 562 pages
From the Back Cover
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.
Most helpful customer reviews
14 of 16 people found the following review helpful.
The canonical book of random matrices
By A Customer
Mehta's book is the book that gets refered to in every article that deals with random matrices. It covers classical theory of random matrices well, but omits many important developments such as chiral random matrices. 'Random matrices' is somewhat pricey but it is nevertheless the best book there is on theory of random matrices. Unfortunately.
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