Local law of free addition of random matrices

 概率统计学术报告（2019-6-25）

Title:  Local law of free addition of random matrices

Speaker:  Dr.  Zhigan Bao  (鲍志刚)  香港科技大学

Time:  3:00pm,  2019-6-25

Location:  4F ，Sir R. R. Shaw Building，Yuquan Campus,  Zhejiang University

Abstract:  The eigenvalue distribution of the sum of two large Hermitian matrices, when one of them is conjugated by a Haar distributed unitary matrix, is asymptotically given by the free additive convolution of their spectral distributions. In this talk, I will show that this convergence also holds locally, down to the optimal scales larger than the eigenvalue spacing.  This implies optimal rigidity of the eigenvalues and optimal rate of convergence in Voiculescu’s theorem. An extension of our method also gives the optimal local single ring theorem. This talk is based on the joint work with Laszlo Erdos and Kevin Schnelli

All are welcome!

Contact Person: Zhonggen Su （苏中根）, 

suzhonggen@zju.edu.cn,  13588731705

                                   浙江大学统计研究所

                                        2019-6-14