Annealed and quenched limit theorems for random expanding dynamical systems

Abstract

In this paper, we investigate annealed and quenched limit theorems for random expanding dynamical systems. Making use of functional analytic techniques and more probabilistic arguments with martingales, we prove annealed versions of a central limit theorem, a large deviation principle, a local limit theorem, and an almost sure invariance principle. We also discuss the quenched central limit theorem, dynamical Borel-Cantelli lemmas, Erdös-Rényi laws and concentration inequalities.

Appeared online in Probability Theory and Related Fields