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Author : Colin L. Mallows
Publisher :
ISBN 13 :
Total Pages : 0 pages
Book Rating : 4.:/5 (134 download)
Download or read book Latent Roots and Vectors of Random Matrices written by Colin L. Mallows and published by . This book was released on 1959 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Giacomo Livan
Publisher : Springer
ISBN 13 : 3319708856
Total Pages : 122 pages
Book Rating : 4.3/5 (197 download)
Download or read book Introduction to Random Matrices written by Giacomo Livan and published by Springer. This book was released on 2018-01-16 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: Modern developments of Random Matrix Theory as well as pedagogical approaches to the standard core of the discipline are surprisingly hard to find in a well-organized, readable and user-friendly fashion. This slim and agile book, written in a pedagogical and hands-on style, without sacrificing formal rigor fills this gap. It brings Ph.D. students in Physics, as well as more senior practitioners, through the standard tools and results on random matrices, with an eye on most recent developments that are not usually covered in introductory texts. The focus is mainly on random matrices with real spectrum.The main guiding threads throughout the book are the Gaussian Ensembles. In particular, Wigner’s semicircle law is derived multiple times to illustrate several techniques (e.g., Coulomb gas approach, replica theory).Most chapters are accompanied by Matlab codes (stored in an online repository) to guide readers through the numerical check of most analytical results.
Author : Joel E. Cohen
Publisher : American Mathematical Soc.
ISBN 13 : 082185044X
Total Pages : 376 pages
Book Rating : 4.8/5 (218 download)
Download or read book Random Matrices and Their Applications written by Joel E. Cohen and published by American Mathematical Soc.. This book was released on 1986 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt: Features twenty-six expository papers on random matrices and products of random matrices. This work reflects both theoretical and applied concerns in fields as diverse as computer science, probability theory, mathematical physics, and population biology.
Author : M. L. Mehta
Publisher : Academic Press
ISBN 13 : 1483258564
Total Pages : 270 pages
Book Rating : 4.4/5 (832 download)
Download or read book Random Matrices and the Statistical Theory of Energy Levels written by M. L. Mehta and published by Academic Press. This book was released on 2014-05-12 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Matrices and the Statistical Theory of Energy Levels focuses on the processes, methodologies, calculations, and approaches involved in random matrices and the statistical theory of energy levels, including ensembles and density and correlation functions. The publication first elaborates on the joint probability density function for the matrix elements and eigenvalues, including the Gaussian unitary, symplectic, and orthogonal ensembles and time-reversal invariance. The text then examines the Gaussian ensembles, as well as the asymptotic formula for the level density and partition function. The manuscript elaborates on the Brownian motion model, circuit ensembles, correlation functions, thermodynamics, and spacing distribution of circular ensembles. Topics include continuum model for the spacing distribution, thermodynamic quantities, joint probability density function for the eigenvalues, stationary and nonstationary ensembles, and ensemble averages. The publication then examines the joint probability density functions for two nearby spacings and invariance hypothesis and matrix element correlations. The text is a valuable source of data for researchers interested in random matrices and the statistical theory of energy levels.
Author : Alice Guionnet
Publisher : Springer
ISBN 13 : 3540698973
Total Pages : 296 pages
Book Rating : 4.5/5 (46 download)
Download or read book Large Random Matrices: Lectures on Macroscopic Asymptotics written by Alice Guionnet and published by Springer. This book was released on 2009-04-20 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory has developed in the last few years, in connection with various fields of mathematics and physics. These notes emphasize the relation with the problem of enumerating complicated graphs, and the related large deviations questions. Such questions are also closely related with the asymptotic distribution of matrices, which is naturally defined in the context of free probability and operator algebra. The material of this volume is based on a series of nine lectures given at the Saint-Flour Probability Summer School 2006. Lectures were also given by Maury Bramson and Steffen Lauritzen.
Author : Leonid Andreevich Pastur
Publisher : American Mathematical Soc.
ISBN 13 : 082185285X
Total Pages : 650 pages
Book Rating : 4.8/5 (218 download)
Download or read book Eigenvalue Distribution of Large Random Matrices written by Leonid Andreevich Pastur and published by American Mathematical Soc.. This book was released on 2011 with total page 650 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrix theory is a wide and growing field with a variety of concepts, results, and techniques and a vast range of applications in mathematics and the related sciences. The book, written by well-known experts, offers beginners a fairly balanced collection of basic facts and methods (Part 1 on classical ensembles) and presents experts with an exposition of recent advances in the subject (Parts 2 and 3 on invariant ensembles and ensembles with independent entries). The text includes many of the authors' results and methods on several main aspects of the theory, thus allowing them to present a unique and personal perspective on the subject and to cover many topics using a unified approach essentially based on the Stieltjes transform and orthogonal polynomials. The exposition is supplemented by numerous comments, remarks, and problems. This results in a book that presents a detailed and self-contained treatment of the basic random matrix ensembles and asymptotic regimes. This book will be an important reference for researchers in a variety of areas of mathematics and mathematical physics. Various chapters of the book can be used for graduate courses; the main prerequisite is a basic knowledge of calculus, linear algebra, and probability theory.
Author : Sven J. Hammarling
Publisher :
ISBN 13 : 9780852741511
Total Pages : 172 pages
Book Rating : 4.7/5 (415 download)
Download or read book Latent Roots and Latent Vectors written by Sven J. Hammarling and published by . This book was released on 1970 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Mauricio Porto Pato
Publisher : Springer Nature
ISBN 13 : 3031602943
Total Pages : 186 pages
Book Rating : 4.0/5 (316 download)
Download or read book Pseudo-Hermitian Random Matrices written by Mauricio Porto Pato and published by Springer Nature. This book was released on with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Madan Lal Mehta
Publisher : Elsevier
ISBN 13 : 008047411X
Total Pages : 707 pages
Book Rating : 4.0/5 (84 download)
Download or read book Random Matrices written by Madan Lal Mehta and published by Elsevier. This book was released on 2004-10-06 with total page 707 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random Matrices 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
Author :
Publisher :
ISBN 13 :
Total Pages : 574 pages
Book Rating : 4.3/5 (91 download)
Download or read book NBS Special Publication written by and published by . This book was released on 1970 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Édouard Brezin
Publisher : Springer Science & Business Media
ISBN 13 : 140204531X
Total Pages : 519 pages
Book Rating : 4.4/5 (2 download)
Download or read book Applications of Random Matrices in Physics written by Édouard Brezin and published by Springer Science & Business Media. This book was released on 2006-07-03 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: Random matrices are widely and successfully used in physics for almost 60-70 years, beginning with the works of Dyson and Wigner. Although it is an old subject, it is constantly developing into new areas of physics and mathematics. It constitutes now a part of the general culture of a theoretical physicist. Mathematical methods inspired by random matrix theory become more powerful, sophisticated and enjoy rapidly growing applications in physics. Recent examples include the calculation of universal correlations in the mesoscopic system, new applications in disordered and quantum chaotic systems, in combinatorial and growth models, as well as the recent breakthrough, due to the matrix models, in two dimensional gravity and string theory and the non-abelian gauge theories. The book consists of the lectures of the leading specialists and covers rather systematically many of these topics. It can be useful to the specialists in various subjects using random matrices, from PhD students to confirmed scientists.
Author : P. R. Krishnaiah
Publisher :
ISBN 13 :
Total Pages : 27 pages
Book Rating : 4.:/5 (227 download)
Download or read book Simultaneous Tests for Equality of Latent Roots Against Certain Alternatives-ii written by P. R. Krishnaiah and published by . This book was released on 1969 with total page 27 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors proposed a procedure for testing for the equality of latent roots of a matrix, when the associated random matrix has certain distribution, against the alternative that at least two of the roots are unequal. The random matrices considered are (1) Wishart matrix; (2) (S sub 1)(S sub 2)superscript -1; (3) matrix connected with MANOVA; and, (4) matrix associated with canonical correlations; here S sub 1 and S sub 2 are independently distributed central Wishart matrices. (Author).
Author : S. J. Hammarling
Publisher :
ISBN 13 :
Total Pages : 192 pages
Book Rating : 4.:/5 (5 download)
Download or read book Latent Roots and Latent Vectors written by S. J. Hammarling and published by . This book was released on 1970 with total page 192 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author :
Publisher :
ISBN 13 :
Total Pages : 1118 pages
Book Rating : 4.:/5 (319 download)
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1977 with total page 1118 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Nicholas M. Katz
Publisher : American Mathematical Society
ISBN 13 : 1470475073
Total Pages : 441 pages
Book Rating : 4.4/5 (74 download)
Download or read book Random Matrices, Frobenius Eigenvalues, and Monodromy written by Nicholas M. Katz and published by American Mathematical Society. This book was released on 2023-11-13 with total page 441 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main topic of this book is the deep relation between the spacings between zeros of zeta and $L$-functions and spacings between eigenvalues of random elements of large compact classical groups. This relation, the Montgomery-Odlyzko law, is shown to hold for wide classes of zeta and $L$-functions over finite fields. The book draws on and gives accessible accounts of many disparate areas of mathematics, from algebraic geometry, moduli spaces, monodromy, equidistribution, and the Weil conjectures, to probability theory on the compact classical groups in the limit as their dimension goes to infinity and related techniques from orthogonal polynomials and Fredholm determinants.
Author : John Harnad
Publisher : Springer Science & Business Media
ISBN 13 : 1441995145
Total Pages : 536 pages
Book Rating : 4.4/5 (419 download)
Download or read book Random Matrices, Random Processes and Integrable Systems written by John Harnad and published by Springer Science & Business Media. This book was released on 2011-05-06 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the remarkable connections between two domains that, a priori, seem unrelated: Random matrices (together with associated random processes) and integrable systems. The relations between random matrix models and the theory of classical integrable systems have long been studied. These appear mainly in the deformation theory, when parameters characterizing the measures or the domain of localization of the eigenvalues are varied. The resulting differential equations determining the partition function and correlation functions are, remarkably, of the same type as certain equations appearing in the theory of integrable systems. They may be analyzed effectively through methods based upon the Riemann-Hilbert problem of analytic function theory and by related approaches to the study of nonlinear asymptotics in the large N limit. Associated with studies of matrix models are certain stochastic processes, the "Dyson processes", and their continuum diffusion limits, which govern the spectrum in random matrix ensembles, and may also be studied by related methods. Random Matrices, Random Processes and Integrable Systems provides an in-depth examination of random matrices with applications over a vast variety of domains, including multivariate statistics, random growth models, and many others. Leaders in the field apply the theory of integrable systems to the solution of fundamental problems in random systems and processes using an interdisciplinary approach that sheds new light on a dynamic topic of current research.
Author : P. R. Krishnaiah
Publisher :
ISBN 13 :
Total Pages : 35 pages
Book Rating : 4.:/5 (227 download)
Download or read book Simultaneous Tests for Equality of Latent Roots Against Certain Alternatives written by P. R. Krishnaiah and published by . This book was released on 1969 with total page 35 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors proposed procedures for testing for equality of latent roots of matrices against some restricted alternatives when the latent roots of the associated random matrices have certain distributions. The random matrices considered are (i) Wishart matrix (ii) (S sub 1) (S sub 2) superscript ( -1) (iii) matrix connected with MANOVA and (iv) matrix associated with canonical correlations; here S sub 1 and S sub 2 are independently distributed central Wishart matrices. (Author).
