EXTREMAL LAWS FOR THE REAL GINIBRE ENSEMBLE

• 成果类型: Article
• 署名作者: Rider, Brian; Sinclair, Christopher D.
• 署名单位: Pennsylvania Commonwealth System of Higher Education (PCSHE); Temple University; University of Oregon
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/13-AAP958
• 发表日期: 2014
• 页码: 1621-1651
• 关键词: random matrices; distributions

摘要

The real Ginibre ensemble refers to the family of n x n matrices in which each entry is an independent Gaussian random variable of mean zero and variance one. Our main result is that the appropriately scaled spectral radius converges in law to a Gumbel distribution as n -> infinity. This fact has been known to hold in the complex and quaternion analogues of the ensemble for some time, with simpler proofs. Along the way we establish a new form for the limit law of the largest real eigenvalue.