Title: Annealed and quenched central limit theorem
for random dynamical systems
Abstract: 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.