CORRELATED RANDOM MATRICES: BAND RIGIDITY AND EDGE UNIVERSALITY

• 成果类型: Article
• 署名作者: Alt, Johannes; Erdos, Laszlo; Krueger, Torben; Schroeder, Dominik
• 署名单位: University of Geneva; Institute of Science & Technology - Austria; University of Bonn
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/19-AOP1379
• 发表日期: 2020
• 页码: 963-1001
• 关键词: spectral statistics; generalized wigner; local statistics; EIGENVALUE; CONVERGENCE

摘要

We prove edge universality for a general class of correlated real symmetric or complex Hermitian Wigner matrices with arbitrary expectation. Our theorem also applies to internal edges of the self-consistent density of states. In particular, we establish a strong form of band rigidity which excludes mismatches between location and label of eigenvalues close to internal edges in these general models.