A spectral approach for quenched limit theorems for random hyperbolic dynamical systems

Abstract

We extend the recent spectral approach for quenched limit theorems developed for piecewise expanding dynamics under general random driving [DrFrGTVa18] to quenched random piecewise hyperbolic dynamics including some classes of billiards. For general ergodic sequences of maps in a neighbourhood of a hyperbolic map we prove a quenched large deviations principle (LDP), central limit theorem (CLT), and local central limit theorem (LCLT).