Spectral Analysis of Large Dimensional Random Matrices

• Main Authors: Bai, Zhidong. (Author), Silverstein, Jack W. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic
• Language: English
• Published: New York, NY : Springer New York, 2010.
• Series: Springer Series in Statistics,
• Subjects: Statistics.; Mathematical statistics.; Statistical Theory and Methods.
• Online Access: https://ezaccess.library.uitm.edu.my/login?url=http://dx.doi.org/10.1007/978-1-4419-0661-8

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 t...

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.