On the quenched central limit theorem for random dynamical systems. (6th May 2016) - Abdelkader, Mohamed; Aimino, Romain
Abstract: We provide a necessary and sufficient condition under which the quenched central limit theorem without random centering holds for one-dimensional random systems that are uniformly expanding. This condition holds in particular when all the maps preserve a common measure. We also give a counter example which shows that this condition is not necessarily satisfied when the maps do not preserve a common measure.