PRODUCTS OF RANDOM MATRICES: DIMENSION AND GROWTH IN NORM

• 成果类型: Article
• 署名作者: Kargin, Vladislav
• 署名单位: Stanford University
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/09-AAP658
• 发表日期: 2010
• 页码: 890-906
• 关键词: theorems

摘要

Suppose that X(1), ... , X(n), ... are i.i.d. rotationally invariant N-by-N matrices. Let Pi(n) = X(n) ... X(1). It is known that n(-1) log vertical bar Pi(n)vertical bar converges to a non-random limit. We prove that under certain additional assumptions on matrices X(i) the speed of convergence to this limit does not decrease when the size of matrices, N, grows.