Spectral Theory of Large Dimensional Random Matrices and Its Applications to Wireless Communications and Finance Statistics

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:

• Introduction
• Limiting Spectral Distributions
• Extreme Eigenvalues
• Central Limit Theorems of Linear Spectral Statistics
• Limiting Behavior of Eigenmatrix of Sample Covariance Matrix
• Wireless Communications
• Limiting Performances of Linear and Iterative Receivers
• Application to Finance

Readership: Graduate students and researchers in random matrices.
Key Features:

• The book introduces basic theorems in large dimensional random matrices emphasizing those which are established under moment conditions and are thus applicable to statistics
• The long proofs of some theorems are omitted and their references have been provided
• Examples of various applications to wireless communications and finance are given