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 analogue  of the log-correlated Gaussian field. This is a joint work with Yukun He.

海报