APPLICATIONS OF MESOSCOPIC CLTS IN RANDOM MATRIX THEORY

• 成果类型: Article
• 署名作者: Landon, Benjamin; Sosoe, Philippe
• 署名单位: Massachusetts Institute of Technology (MIT); Cornell University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/20-AAP1572
• 发表日期: 2020
• 页码: 2769-2795
• 关键词: CENTRAL-LIMIT-THEOREM; linear eigenvalue statistics; fixed-energy universality; generalized wigner

摘要

We present some applications of central limit theorems on mesoscopic scales for random matrices. When combined with the recent theory of homogenization for Dyson Brownian motion, this yields the universality of quantities which depend on the behavior of single eigenvalues of Wigner matrices and beta-ensembles. Among the results we obtain are the Gaussian fluctuations of single eigenvalues for Wigner matrices (without an assumption of 4 matching moments) and classical beta-ensembles (beta = 1, 2, 4), Gaussian fluctuations of the eigenvalue counting function, and an asymptotic expansion up to order o (N-1) for the expected value of eigenvalues in the bulk of the spectrum. The latter result solves a conjecture of Tao and Vu.