An invitation to ${\text{SL}}_2(\mathbb{R})$ cocycles over random dynamics

Abstract

The purpose of these notes is to discuss the advances in the theory of Lyapunov exponents of linear ${\text{SL}}_2(\mathbb{R})$ cocycles over hyperbolic maps. The main focus is around results regarding the positivity of the Lyapunov exponent and the regularity of this function with respect to the underlying data.