FAST APPROACH TO THE TRACY-WIDOM LAW AT THE EDGE OF GOE AND GUE

• 成果类型: Article
• 署名作者: Johnstone, Iain M.; Ma, Zongming
• 署名单位: Stanford University; University of Pennsylvania
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/11-AAP819
• 发表日期: 2012
• 页码: 1962-1988
• 关键词: largest eigenvalue; spacing distributions; RANDOM MATRICES; UNIVERSALITY; POLYNOMIALS; ensembles; LIMITS

摘要

We study the rate of convergence for the largest eigenvalue distributions in the Gaussian unitary and orthogonal ensembles to their Tracy-Widom limits. We show that one can achieve an O(N-2/3.) rate with particular choices of the centering and scaling constants. The arguments here also shed light on more complicated cases of Laguerre and Jacobi ensembles, in both unitary and orthogonal versions. Numerical work shows that the suggested constants yield reasonable approximations, even for surprisingly small values of N.