Spectral Analysis of Large Dimensional Random Matrices van Zhidong Bai and Jack W. Silverstein is an English-language printed textbook. It addresses spectral analysis of high-dimensional random matrices and is intended for students and researchers in mathematics and statistics.
This textbook introduces fundamental concepts, key results, and applied mathematical techniques in the analysis of large-dimensional random matrices. Central to it are moment conditions and probabilistic methods that are applicable within statistics and other scientific fields. Important topics include, among others, Wigner's semicircle law, the Marčenko-Pastur distribution, limits for extreme eigenvalues, and a central limit theorem for linear spectral statistics.
The second edition includes new chapters on the limiting behavior of eigenvectors for sample covariance matrices and applications in wireless communications and finance. The book is practical for researchers and includes mathematical tools such as truncation techniques, matrix identities, and the Stieltjes transform.
In terms of content, the title aligns with topics such as Algebra and mathematics and is part of the Springer Series in Statistics.