EXTREME GAPS BETWEEN EIGENVALUES OF RANDOM MATRICES

• 成果类型: Article
• 署名作者: Ben Arous, Gerard; Bourgade, Paul
• 署名单位: New York University; Harvard University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP710
• 发表日期: 2013
• 页码: 2648-2681
• 关键词: Asymptotics; probability; Spacings; UNIVERSALITY; constant; zeros

摘要

This paper studies the extreme gaps between eigenvalues of random matrices. We give the joint limiting law of the smallest gaps for Haar-distributed unitary matrices and matrices from the Gaussian unitary ensemble. In particular, the kth smallest gap, normalized by a factor n(-4/3), has a limiting density proportional to x(3k-1)e(-x3). Concerning the largest gaps, normalized by n/root log n, they converge in L-p to a constant for all p > 0. These results are compared with the extreme gaps between zeros of the Riemann zeta function.