BEYOND UNIVERSALITY IN RANDOM MATRIX THEORY

• 成果类型: Article
• 署名作者: Edelman, Alan; Guionnet, A.; Peche, S.
• 署名单位: Massachusetts Institute of Technology (MIT); Universite Paris Cite
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/15-AAP1129
• 发表日期: 2016
• 页码: 1659-1697
• 关键词: sample covariance matrices; expected spectral distributions; generalized wigner matrices; spacing distributions; convergence rate; statistics; eigenvalues; ensembles; limit; clt

摘要

In order to have a better understanding of finite random matrices with non-Gaussian entries, we study the 1/N expansion of local eigenvalue statistics in both the bulk and at the hard edge of the spectrum of random matrices. This gives valuable information about the smallest singular value not seen in universality laws. In particular, we show the dependence on the fourth moment (or the kurtosis) of the entries. This work makes use of the so-called complex Gaussian divisible ensembles for both Wigner and sample covariance matrices.