Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6979338653
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