Spectral Analysis of Large Dimensional Random Matrices, 2nd edn

Today’s statistical landscape is assuredly multi-dimensional. With the advent of very high dimensional data in physics, in biostatistics and in mathematical finance, statisticians have been increasingly aware of the inadequacy of classical limit theorems when dealing with high dimensional data sets. New asymptotic results are therefore required to tackle these problems. A modern perspective on high dimensional data that has gained traction in the last three decades is random-matrix theory. A random matrix is a matrix-valued random variable, and random-matrix theory is essentially concerned with the study of the asymptotic properties of matrix-valued random variables. Much of the original interest in random matrices stems from applications in theoretical physics, where random matrices were introduced in the context of quantum mechanics. This volume constitutes the second edition of a popular reference text on several important results on the asymptotic spectral properties of random matrices, written by two leading authors on this subject. In the 1980s, major contributions to the existence of limiting spectral distributions were made, and this text summarizes these developments in a unified manner. Albeit mainly theoretical, this volume also contains a chapter dedicated to applications, which include sections on wireless communications, different types of channel models and some applications to mathematical finance. With this impressive compendium of theoretical results, Bai and Silverstein provide a landmark text, which is likely to pave the way for further theoretical and applied developments in this field. In particular, one of the substantial qualities of this monograph is that the authors have voluntarily striven to provide detailed proofs, which should allow new researchers to acquire a solid theoretical basis in random-matrix spectral theory. This book is therefore recommended to both experienced researchers in random-matrix theory and theoretically inclined graduate students who are interested in this growing field of statistical enquiry.