Quenched limit theorems for random U(1) extensions of expanding maps

Abstract

The Lyapunov spectra of random U(1) extensions of expanding maps on the torus were investigated in our previous work [NW2015]. Using the result, we extend the recent spectral approach for quenched limit theorems for expanding maps [DFGV2018] and hyperbolic maps [DFGV2019] to our partially hyperbolic dynamics. Quenched central limit theorems, large deviations principles and local central limit theorems for random U(1) extensions of expanding maps on the torus are proved via corresponding theorems for abstract random dynamical systems.