ON CRAMER-VON MISES STATISTIC FOR THE SPECTRAL DISTRIBUTION OF RANDOM MATRICES

• 成果类型: Article
• 署名作者: Bao, Zhigang; He, Yukun
• 署名单位: Hong Kong University of Science & Technology; City University of Hong Kong
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/22-AAP1788
• 发表日期: 2022
• 页码: 4315-4355
• 关键词: eigenvalues; maximum; fluctuations; CONVERGENCE; rates

摘要

Let FN and F be the empirical and limiting spectral distributions of an N x N Wigner matrix. The Cramer-von Mises (CvM) statistic is a classical goodness-of-fit statistic that characterizes the distance between FN and F in L2-norm. In this paper, we consider a mesoscopic approximation of the CvM statistic for Wigner matrices, and derive its limiting distribution. In the Appendix, we also give the limiting distribution of the CvM statistic (without approximation) for the toy model CUE.