Random 2D linear cocycles II: statistical properties
Dynamical Systems
2025-10-16 v2 Mathematical Physics
math.MP
Abstract
Consider the space of two dimensional random linear cocycles over a shift in finitely many symbols, with at least one singular and one invertible matrix. We provide an explicit formula for the unique stationary measure associated to such cocycles and establish a Furstenberg-type formula characterizing the Lyapunov exponent. Using the spectral properties of the corresponding Markov operator and a parameter elimination argument, we prove that Lebesgue almost every cocycle in this space satisfies large deviations estimates and a central limit theorem.
Cite
@article{arxiv.2505.00146,
title = {Random 2D linear cocycles II: statistical properties},
author = {Pedro Duarte and Marcelo Durães and Tomé Graxinha and Silvius Klein},
journal= {arXiv preprint arXiv:2505.00146},
year = {2025}
}
Comments
45 pages