"随机矩阵"就是由某些概率空间下的随机变量作为元素的矩阵，随机矩阵谱理论主要是研究在满足某些条件时随机矩阵的特征根的性质。本项目主要研究大维随机矩阵经验谱分布函数的收敛及其在多元统计分析与无线通讯中的应用，其中包括：大维随机矩阵经验谱分布函数的收敛速度，大维随机矩阵线形谱统计量的中心极限定理及其在多元统计分析中的应用以及大维随机矩阵谱理论在无线通讯中的应用。其中涉及的矩阵类型包括Wigner矩阵、样本协方差矩阵、F矩阵和Beta矩阵。

In probability theory and mathematical physics, a random matrix is a matrix-valued random variable. Many important properties of physical systems can be represented mathematically as matrix problems. In this project we will investigate the congvergence of the empirical spectral distribution of large dimensional random matrices and its applications in multivariate statistical analysis and wireless communications. That includes the convergence rates of the empirical spectral distribution of large dimensional random matrices,the CLT of linear spectral statistics of large dimensional random matrices and their applications in multivariate statistical analysis and wireless communications. We will consider four types of random matrices which are Wigner matrices, sample covariance matrices, F matrices and Beta matrices.