Non-stationary version of Furstenberg Theorem on random matrix products

2022/10/07 by Anton Gorodetski, Victor Kleptsyn, Gorodetski, Anton +1 · 4 citations
Decision Sciences · Mathematics · #37A50 #37H15 #60B20 #60F10 #60F15 #Dynamical Systems (math.DS) #FOS: Mathematics #Probability (math.PR) #Probability and Risk Models #Random Matrices and Applications #Stochastic processes and statistical mechanics

paper · doi:10.48550/arxiv.2210.03805

openalex publication_date 2022/10/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove a non-stationary analog of the Furstenberg Theorem on random matrix products (that can be considered as a matrix version of the law of large numbers). Namely, under a suitable genericity conditions the sequence of norms of random products of independent but not necessarily identically distributed \SL(d, ℝ) matrices grow exponentially fast, and there exists a non-random sequence that almost surely describes asymptotical behaviour of that sequence.

Cited by

• Localization of the 1D Non-Stationary Anderson Model
• Limit theorems for inhomogeneous random walks on GL(d,\mathbb R)
• The fibered rotation number
• Effective Gaps between singular values of non-stationary matrix products subject to non-degenerate noise

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