Abstract:The problems that we consider in this paper are as follows. Let $A_1, \ldots, A_k$ be square matrices (over reals). Let $W=w(A_1, \ldots, A_k)$ be a random product of $n$ matrices. What is the expected growth rate of the largest (in the absolute value) entry in such a random product? What is the (maximal) Lyapunov exponent for a random matrix product like that? We give an answer to the first question under some mild restrictions on the entries of $A_i$. For the second question, we offer a very simple and efficient method to produce an upper bound on the Lyapunov exponent.
From: Vladimir Shpilrain [view email]
[v1]
Tue, 23 Sep 2025 12:56:42 UTC (7 KB)
[v2]
Wed, 7 Jan 2026 05:36:54 UTC (8 KB)
[v3]
Fri, 1 May 2026 16:20:43 UTC (8 KB)
[v4]
Tue, 2 Jun 2026 11:54:34 UTC (8 KB)
[v5]
Tue, 28 Jul 2026 08:47:31 UTC (9 KB)
此内容由惯性聚合(RSS阅读器)自动聚合整理，仅供阅读参考。 原文来自 — 版权归原作者所有。