题目：Spectral Radius and Empirical Law of Product Ensemble

报告人：ProfessorYongchengQi，University of Minnesota Duluth

时间：2017年6月28日下午4:00--5:00

地点：理科楼A304

摘要：In this talk we investigate asymptotic properties of the eigenvalues from two n by n random matrices as n goes to infinity. The first one is the product of mi.i.d. (complex)Ginibreensembles, and the second one is that of truncations of m independentHaarunitary matrices which may have different sizes. For the product ofGinibreensembles, limiting distributions of the spectral radii are obtained when the limit of m/n exists, and explicit empirical distributions of the eigenvalues are obtained regardless of the speed of m compared to n. For the product of truncations ofHaarunitary matrices, limits of the empirical distributions are quite rich, depending on m and sizes ofHaarunitary matrices. The main techniques we employ are the independence structure of points following a determinantalpoint process and some estimations of moments for sum of functions of the eigenvalues.

联系人： 杨瑛