MESOSCOPIC EIGENVALUE STATISTICS OF WIGNER MATRICES

• 成果类型: Article
• 署名作者: He, Yukun; Knowles, Antti
• 署名单位: Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/16-AAP1237
• 发表日期: 2017
• 页码: 1510-1550
• 关键词: altshuler-shklovskii formulas; UNIVERSALITY

摘要

We prove that the linear statistics of the eigenvalues of a Wigner matrix converge to a universal Gaussian process on all mesoscopic spectral scales, that is, scales larger than the typical eigenvalue spacing and smaller than the global extent of the spectrum.