ON THE RIGHTMOST EIGENVALUE OF NON-HERMITIAN RANDOM MATRICES

• 成果类型: Article
• 署名作者: Cipolloni, Giorgio; Erdos, Laszlo; Schroeder, Dominik; Xu, Yuanyuan
• 署名单位: Princeton University; Institute of Science & Technology - Austria; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/23-AOP1643
• 发表日期: 2023
• 页码: 2192-2242
• 关键词: spectral-radius; circular law; tracy-widom; statistics; UNIVERSALITY; maximum; fluctuations; chaos

摘要

We establish a precise three-term asymptotic expansion, with an optimal estimate of the error term, for the rightmost eigenvalue of an n x n random matrix with independent identically distributed complex entries as n tends to infinity. All terms in the expansion are universal.