ASYMPTOTIC LYAPUNOV EXPONENTS FOR LARGE RANDOM MATRICES

• 成果类型: Article
• 署名作者: Nguyen, Hoi H.
• 署名单位: University System of Ohio; Ohio State University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/17-AAP1293
• 发表日期: 2017
• 页码: 3672-3705
• 关键词: LITTLEWOOD-OFFORD PROBLEM; PRODUCTS; localization; LAW

摘要

Suppose that A(1),..., A(N) are independent random matrices of size n whose entries are i.i.d. copies of a random variable xi of mean zero and variance one. It is known from the late 1980s that when xi is Gaussian then N-1 log parallel to A(N)... A(1) parallel to converges to log root n as N -> 8. We will establish similar results for more general matrices with explicit rate of convergence. Our method relies on a simple interplay between additive structures and growth of matrices.