Limit theorems for random non-uniformly expanding or hyperbolic maps with exponential tails

Abstract

We prove a Berry-Esseen theorem, a local central limit theorem and (local) large and (global) moderate deviations principles for i.i.d. (uniformly) random non-uniformly expanding or hyperbolic maps with exponential first return times. Using existing results the problem is reduced to certain random tower extension in the sense of Young, which is the main focus of this paper. On the random towers we will obtain our results using contraction properties of random complex equivariant cones with respect to the complex Hilbert projective metric.