Spectral theory of large dimensional random matrices and its applications to wireless communications and finance: random matrix theory and its applications

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.Contents:IntroductionLimiting Spectral DistributionsExtreme EigenvaluesCentral Limit Theorems of Linear Spectral StatisticsLimiting Behavior of Eigenmatrix of Sample Covariance MatrixWireless CommunicationsLimiting Performances of Linear and Iterative ReceiversApplication to FinanceReadership: Graduate students and researchers in random matrices.