Edge universality for non-Hermitian random matrices

• 成果类型: Article
• 署名作者: Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik
• 署名单位: Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-020-01003-7
• 发表日期: 2021
• 页码: 1-28
• 关键词: eigenvalue statistics; bulk universality; spectral-radius; real; ensembles; distributions

摘要

We consider large non-Hermitian real or complex random matrices X with independent, identically distributed centred entries. We prove that their local eigenvalue statistics near the spectral edge, the unit circle, coincide with those of the Ginibre ensemble, i.e. when the matrix elements of X are Gaussian. This result is the non-Hermitian counterpart of the universality of the Tracy-Widom distribution at the spectral edges of the Wigner ensemble.