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arXiv · 2505.00146

Random 2D linear cocycles II: statistical properties

Pedro Duarte·Marcelo Durães·Tomé Graxinha·Silvius Klein
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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.

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Pedro Duarte, Marcelo Durães, Tomé Graxinha, Silvius Klein. 2025-04-30. Random 2D linear cocycles II: statistical properties. https://arxiv.org/abs/2505.00146

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