THE TOP EIGENVALUE OF THE RANDOM TOEPLITZ MATRIX AND THE SINE KERNEL

• 成果类型: Article
• 署名作者: Sen, Arnab; Virag, Balint
• 署名单位: University of Minnesota System; University of Minnesota Twin Cities; University of Toronto; University of Toronto
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/13-AOP863
• 发表日期: 2013
• 页码: 4050-4079
• 关键词: dimensional random matrices; spectral norm; hankel

摘要

We show that the top eigenvalue of an n x n random symmetric Toeplitz matrix, scaled by v root 2n log n, converges to the square of the 2 -> 4 operator norm of the sine kernel.