Spectral Radius and Empirical Law of Product Ensemble


题目 Spectral Radius and Empirical Law of Product Ensemble

报告人:Professor Yongcheng Qi University of Minnesota Duluth




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 m i.i.d. (complex) Ginibre ensembles, and the second one is that  of truncations of m independent Haar unitary matrices which may have  different sizes. For the product of Ginibre ensembles, 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 of Haar unitary matrices, limits of the empirical distributions  are quite rich, depending on m and sizes of Haar unitary matrices. The main  techniques we employ are the independence structure of points following a  determinantal point process and some estimations of moments for sum of  functions of the eigenvalues.


联系人: 杨瑛


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