Furstenberg Theory for Singular Cocycles

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.

This is a joint work with Pedro Duarte, Tomé Graxinha and Silvius Klein.

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There will be a coffee break after the seminar.