【Academic Seminar】On Cramer-von Mises Statistic for the Spectral Distribution of Random Matrices - Prof. Zhigang Bao

Topic: On Cramer-von Mises Statistic for the Spectral Distribution of Random Matrices

Speaker: Prof. Zhigang Bao, The Hong Kong University of Science and Technology

Date and Time: 15:30 - 16:30, Friday, November 1, 2019

Venue: Boardroom, Dao Yuan Building

Abstract：

Let F_n and F be the empirical and limiting spectral distributions of an n by n Wigner matrix. The Cramer-von Mises (CvM) statistic is a classical goodness-of-fit statistic that characterizes the distance between F_n and F in l^2-norm. In this talk, we will consider a mesoscopic approximation of the CvM statistic for Wigner matrices, and derive its limiting distribution. The distribution fits well the heuristic prediction given by the log-correlated Gaussian field approximation for the stochastic filed of F_n(t). This is a joint work with Yukun He.

Biography：

Prof. Zhigang Bao is an Assistant Professor at the Hong Kong University of Science and Technology. He got his PhD degree in the Department of Mathematics, Zhejiang University, supervised by Prof. Zhonggen Su. Before that, he got his Bachelor's degree from Zhejiang University in 2013. He is interested in Probability, Statistical Physics, and Mathematical Statistics in general. In specific, his research interests are Random Matrix Theory, High Dimensional Statistics, Free Probability Theory, Supersymmetry Method, Disordered Quantum Systems and KPZ Universality. (see his personal page for details: http://mazgbao.people.ust.hk/)