Random Matrices, Volume 142, Third Edition (Pure and Applied Mathematics) [Hardcover]

Madan Lal Mehta (Author)

Book Description

ISBN-10: 0120884097 | ISBN-13: 978-0120884094 | Publication Date: November 16, 2004 | Edition: 3

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.

Editorial Reviews

Book Description

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

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. --This text refers to an out of print or unavailable edition of this title.

Product Details

• Hardcover: 706 pages
• Publisher: Academic Press; 3 edition (November 16, 2004)
• Language: English
• ISBN-10: 0120884097
• ISBN-13: 978-0120884094
• Product Dimensions: 9 x 6.2 x 1.3 inches
• Shipping Weight: 2.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (1 customer review)
• Amazon Best Sellers Rank: #77,027 in Books (See Top 100 in Books)

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Most Helpful Customer Reviews

12 of 14 people found the following review helpful:

4.0 out of 5 stars The canonical book of random matrices, April 14, 2000

By A Customer

This review is from: Random Matrices, Second Edition: Revised and Enlarged Second Edition (Pure and Applied Mathematics) (Hardcover)

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.