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Spectral Analysis of Large Dimensional Random Matrices / Edition 2
     

Spectral Analysis of Large Dimensional Random Matrices / Edition 2

by Zhidong Bai, Jack W. Silverstein
 

ISBN-10: 1441906606

ISBN-13: 9781441906601

Pub. Date: 12/21/2009

Publisher: Springer New York

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

Overview

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.
Zhidong Bai is a professor of the School of Mathematics and Statistics at Northeast Normal University and Department of Statistics and Applied Probability at National University of Singapore. He is a Fellow of the Third World Academy of Sciences and a Fellow of the Institute of Mathematical Statistics.
Jack W. Silverstein is a professor in the Department of Mathematics at North Carolina State University. He is a Fellow of the Institute of Mathematical Statistics.

Product Details

ISBN-13:
9781441906601
Publisher:
Springer New York
Publication date:
12/21/2009
Series:
Springer Series in Statistics , #126
Edition description:
2nd ed. 2010
Pages:
552
Product dimensions:
6.40(w) x 9.30(h) x 1.50(d)

Table of Contents

Introduction.- Wigner matrices and semicircular law.- Sample covariance matrices and the Marcenko-Pastur law.- Product of two random matrices.- Limits of extreme eigenvalues.- Spectrum separation.- Semicircle law for Hadamard products.- Convergence rates of ESD.- CLT for linear spectral statistics.- Eigenvectors of sample covariance matrices.- Circular law.- Some applications of RMT.

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