Spectral analysis of large dimensional random matrices

By: Zhidong BaiContributor(s): Jack W. SilversteinMaterial type: TextTextSeries: Springer Series in StatisticsPublication details: New York: Springer, [c2010]Description: 551 pISBN: 9781441906601LOC classification: QA 188
Contents:
1. Introduction 2. Wigner Matrices and Semicircular Law 3. Sample Covariance Matrices and the Marčenko-Pastur Law 4. Product of Two Random Matrices 5. Limits of Extreme Eigenvalues 6. Spectrum Separation 7. Semicircular Law for Hadamard Products 8. Convergence Rates of ESD 9. CLT for Linear Spectral Statistics 10. Eigenvectors of Sample Covariance Matrices 11. Circular Law 12. Some Applications of RMT
Summary: 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. --- summary provided by publisher
Tags from this library: No tags from this library for this title. Log in to add tags.
    Average rating: 0.0 (0 votes)
Item type Current library Collection Shelving location Call number Status Notes Date due Barcode Item holds
Book Book ICTS
Mathematic Rack No 4 QA 188 (Browse shelf (Opens below)) Available Invoice no. IN 1199 ; Date: 09-12-2019 02312
Total holds: 0

1. Introduction
2. Wigner Matrices and Semicircular Law
3. Sample Covariance Matrices and the Marčenko-Pastur Law
4. Product of Two Random Matrices
5. Limits of Extreme Eigenvalues
6. Spectrum Separation
7. Semicircular Law for Hadamard Products
8. Convergence Rates of ESD
9. CLT for Linear Spectral Statistics
10. Eigenvectors of Sample Covariance Matrices
11. Circular Law
12. Some Applications of RMT

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. --- summary provided by publisher

There are no comments on this title.

to post a comment.