Large Random Matrices
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Eigenvalue Distribution Of Large Random Matrices
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Author : Leonid Andreevich Pastur
language : en
Publisher: American Mathematical Soc.
Release Date :
Eigenvalue Distribution Of Large Random Matrices written by Leonid Andreevich Pastur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
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. This book offers beginners a fairly balanced collection of basic facts and methods.
Large Random Matrices
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Author : Alice Guionnet
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-25
Large Random Matrices written by Alice Guionnet and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-25 with Mathematics categories.
These lectures emphasize the relation between the problem of enumerating complicated graphs and the related large deviations questions. Such questions are closely related with the asymptotic distribution of matrices.
Eigenvalue Distribution Of Large Random Matrices
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Author : Leonid Andreevich Pastur
language : en
Publisher: American Mathematical Soc.
Release Date : 2011
Eigenvalue Distribution Of Large Random Matrices written by Leonid Andreevich Pastur and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Mathematics categories.
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.
Spectral Analysis Of Large Dimensional Random Matrices
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Author : Zhidong Bai
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-12-10
Spectral Analysis Of Large Dimensional Random Matrices written by Zhidong Bai and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-12-10 with Mathematics categories.
The aim of the book is to introduce basic concepts, main results, and widely applied mathematical tools in the spectral analysis of large dimensional random matrices. The core of the book focuses on results established under moment conditions on random variables using probabilistic methods, and is thus easily applicable to statistics and other areas of science. The book introduces fundamental results, most of them investigated by the authors, such as the semicircular law of Wigner matrices, the Marcenko-Pastur law, the limiting spectral distribution of the multivariate F matrix, limits of extreme eigenvalues, spectrum separation theorems, convergence rates of empirical distributions, central limit theorems of linear spectral statistics, and the partial solution of the famous circular law. While deriving the main results, the book simultaneously emphasizes the ideas and methodologies of the fundamental mathematical tools, among them being: truncation techniques, matrix identities, moment convergence theorems, and the Stieltjes transform. Its treatment is especially fitting to the needs of mathematics and statistics graduate students and beginning researchers, having a basic knowledge of matrix theory and an understanding of probability theory at the graduate level, who desire to learn the concepts and tools in solving problems in this area. It can also serve as a detailed handbook on results of large dimensional random matrices for practical users. This second edition includes two additional chapters, one on the authors' results on the limiting behavior of eigenvectors of sample covariance matrices, another on applications to wireless communications and finance. While attempting to bring this edition up-to-date on recent work, it also provides summaries of other areas which are typically considered part of the general field of random matrix theory.
A Dynamical Approach To Random Matrix Theory
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Author : László Erdős
language : en
Publisher: American Mathematical Soc.
Release Date : 2017-08-30
A Dynamical Approach To Random Matrix Theory written by László Erdős and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-08-30 with Mathematics categories.
A co-publication of the AMS and the Courant Institute of Mathematical Sciences at New York University This book is a concise and self-contained introduction of recent techniques to prove local spectral universality for large random matrices. Random matrix theory is a fast expanding research area, and this book mainly focuses on the methods that the authors participated in developing over the past few years. Many other interesting topics are not included, and neither are several new developments within the framework of these methods. The authors have chosen instead to present key concepts that they believe are the core of these methods and should be relevant for future applications. They keep technicalities to a minimum to make the book accessible to graduate students. With this in mind, they include in this book the basic notions and tools for high-dimensional analysis, such as large deviation, entropy, Dirichlet form, and the logarithmic Sobolev inequality. This manuscript has been developed and continuously improved over the last five years. The authors have taught this material in several regular graduate courses at Harvard, Munich, and Vienna, in addition to various summer schools and short courses. Titles in this series are co-published with the Courant Institute of Mathematical Sciences at New York University.
Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics Random Matrix Theory And Its Applications
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Author : Zhaoben Fang
language : en
Publisher: World Scientific
Release Date : 2014-01-24
Spectral Theory Of Large Dimensional Random Matrices And Its Applications To Wireless Communications And Finance Statistics Random Matrix Theory And Its Applications written by Zhaoben Fang and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-24 with Mathematics categories.
The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.
Random Matrices And Their Applications
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Author : Joel E. Cohen
language : en
Publisher: American Mathematical Soc.
Release Date : 1986
Random Matrices And Their Applications written by Joel E. Cohen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1986 with Mathematics categories.
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.
Smart Grid Using Big Data Analytics
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Author : Robert C. Qiu
language : en
Publisher: John Wiley & Sons
Release Date : 2017-04-17
Smart Grid Using Big Data Analytics written by Robert C. Qiu and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-17 with Technology & Engineering categories.
This book is aimed at students in communications and signal processing who want to extend their skills in the energy area. It describes power systems and why these backgrounds are so useful to smart grid, wireless communications being very different to traditional wireline communications.
Random Matrix Methods For Machine Learning
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Author : Romain Couillet
language : en
Publisher: Cambridge University Press
Release Date : 2022-07-21
Random Matrix Methods For Machine Learning written by Romain Couillet and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-07-21 with Computers categories.
This unified random matrix approach to large-dimensional machine learning covers applications from power detection to deep neural networks.
Random Matrix Theory And Its Applications Multivariate Statistics And Wireless Communications
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Author : Zhidong Bai
language : en
Publisher: World Scientific
Release Date : 2009-07-27
Random Matrix Theory And Its Applications Multivariate Statistics And Wireless Communications written by Zhidong Bai and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-27 with Mathematics categories.
Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.