The book contains three parts: Spectral theory of large dimensional random matrices; Applications to wireless communications; and Applications to finance. In the first part, we introduce some basic theorems of spectral analysis of large dimensional random matrices that are obtained under finite moment conditions, such as the limiting spectral distributions of Wigner matrix and that of large dimensional sample covariance matrix, limits of extreme eigenvalues, and the central limit theorems for linear spectral statistics. In the second part, we introduce some basic examples of applications of random matrix theory to wireless communications and in the third part, we present some examples of Applications to statistical finance.

Random matrix theory has a long history, beginning in the first instance in multivariate statistics. It was used by Wigner to supply explanations for the important regularity features of the apparently random dispositions of the energy levels of heavy nuclei. The subject was further deeply developed under the important leadership of Dyson, Gaudin and Mehta, and other mathematical physicists.

In the early 1990s, random matrix theory witnessed applications in string theory and deep connections with operator theory, and the integrable systems were established by Tracy and Widom. More recently, the subject has seen applications in such diverse areas as large dimensional data analysis and wireless communications.

This volume contains chapters written by the leading participants in the field which will serve as a valuable introduction into this very exciting area of research.

This open access book, authored by a world-leading researcher in this field, describes fundamentals of dynamic spectrum management, provides a systematic overview on the enabling technologies covering cognitive radio, blockchain, and artificial intelligence, and offers valuable guidance for designing advanced wireless communications systems. This book is intended for a broad range of readers, including students and professionals in this field, as well as radio spectrum policy makers.

This open access book, authored by a world-leading researcher in this field, describes fundamentals of dynamic spectrum management, provides a systematic overview on the enabling technologies covering cognitive radio, blockchain, and artificial intelligence, and offers valuable guidance for designing advanced wireless communications systems. This book is intended for a broad range of readers, including students and professionals in this field, as well as radio spectrum policy makers.