Non-stationary version of Furstenberg's Theorem on random matrix products

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, we prove that under 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 the asymptotic behaviour of the norms of random products.