随机矩阵理论是目前国内外十分热门的研究领域，在物理，数学和无线通讯等有着广泛的应用。本项目主要利用可积系统，正交多项式理论和Riemann-Hilbert方法等现代数学工具研究无线通讯模型中大维数随机矩阵有关统计量的分布及其一致渐近：1.基于非线性速降法和Painleve方程，研究随机矩阵极端特征值分布的一致渐近。2.基于可积系统的方法和Riemann-Hilbert方法，研究随机矩阵极端特征值比值分布与可积系统Tau函数的关系及其一致渐近。3.基于正交多项式，可积系统和Riemann-Hilbert方法，研究随机矩阵条件数分布的可积结构及其一致渐近性。将上述结果应用于无线通讯频谱感知算法。

Random matrix theory was introduced to the theoretical physics community in 1950s. Since that time, it not only has became extremely active in many research fileds such as mathematics and physics but also has many important applications in wireless communication.Based on some modern mathematical methods in integrable systems, orthogonal polynomials and Riemann-Hilbert approach, the core of this porject is to study analytical properties of related statistics of large dimensional random matrices in wireless communication model.There are three objects as follows: 1.With the aid of nonlinear steepest descent method and Painleve equations, we study uniform asymptotics of the extreme eigenvalues distribution of large dimensional random matrices.2.Based on the theory of integrable systmes and Riemann-Hilbert mehtod,we study the realations between distribution of the extreme eigenvalues ratio of random matrices and tau-functions of integrable systems, and its uniform asymptotics behavior.3.Theories of orthogonal polynomials, integrable systems and Riemann-Hilbert approach are used to study integrable structure of the condtion number distribution of large random matrices, and uniform asymptotics behavior of the distribution.Morover, above results will be applied to spectrum sensing algorithm in wireless communication model.