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 npoint 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 selfcontained and the reader need know mathematics only at the undergraduate level. Key Features * The three Gaussian ensembles, unitary, orthogonal, and symplectic; their npoint 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 To view this DRM protected ebook on your desktop or laptop you will need to have Adobe Digital Editions installed. It is a free software. We also strongly recommend that you sign up for an AdobeID at the Adobe website. For more details please see FAQ 1&2. To view this ebook on an iPhone, iPad or Android mobile device you will need the Adobe Digital Editions app, or BlueFire Reader or Txtr app. These are free, too. For more details see this article.
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Ebook Details 

Pages:  562 
Size:  37.2 MB 
Publisher:  Academic Press 
Date published:  2014 
ISBN:  9781483295954 (DRMPDF)

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Copying:  allowed  Printing:  allowed  Read Aloud:  not allowed 
