Annealed and quenched central limit theorem for random dynamical systems

For random dynamical systems, one can distinguish two kinds of limit theorems: annealed results, which refer to the Birkhoff sums seen as functions of both the phase space variable and the choice of the maps composed, and quenched results, which refer to Birkhoff sums for a fixed, but generic, composition of maps. In this talk, I will describe results about the central limit theorem for random dynamical systems consisting of uniformly expanding maps. In particular, I will show that the annealed central limit theorem is valid for such systems, and I will give a necessary and sufficient condition for its quenched version without random centering to hold. This is a joint work with Matthew Nicol and Sandro Vaienti