Mathematical Sciences: Spectral Theory for Large DimensionalRandom Matrices

研究的主题是大型随机矩阵的谱的渐近理论。要研究的矩阵的类型包括其条目是独立的同分布随机变量的方阵、各种条目相互独立的对称矩阵、以及在特殊情况下是协方差矩阵的一类矩阵。对于这些类型的矩阵中的每一种，涉及随机矩阵的渐近谱分布的问题以及涉及随机矩阵的极值特征值的渐近行为的问题都将被研究。

The topic of research is the asymptotic theory of spectra for large random matrices. The types of matrices to be studied include square matrices whose entries are independent identically distributed random variables, symmetric matrices for which various entries are mutually independent, and matrices of a sort that are covariance matrices in special cases. For each of these types of matrices problems that involve the asymptotic spectral distribution of the random matrix and problems that involve the asymptotic behavior of the extremal eigenvalues for the random matrix will be studied.