Year: 2026
Type: preprint
Abstract: We study products of independent, identically distributed random matrices with an exponential moment and a simple top Lyapunov exponent, without assuming irreducibility. Outside an exceptional invariant subspace called the equator, we establish contraction on average for a weighted projective distance and a spectral gap for the associated Markov operator. We obtain a central limit theorem, a Berry--Esseen bound, deviation estimates near the mean, and an almost sure invariance principle both for the growth of a fixed vector outside the equator and for the operator norm. For fixed vectors, a non-arithmeticity assumption also yields a local limit theorem and a renewal theorem. Our contraction criterion applies more generally to mostly contracting random maps on locally compact spaces with a Lyapunov function, including certain random interval maps.
Source: arXiv (Cornell University)
Authors: Barrientos, Pablo G., Malicet, Dominique
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G1207375514, G7788968503
OpenAlex ID: W7221559337