Random Young Towers and Quenched Limit Laws

Abstract

We obtain quenched almost sure invariance principle for Random Young Tower. We apply our result to i.i.d perturbations of non-uniformly expanding maps. In particular, we answer one open question in [BBMD02]. In Appendix, we also give quenched (functional) central limit theorem for general random dynamical system under an average assumption.

Almost sure invariance principle for random dynamical systems via Gouëzel's approach

“…Moreover, in [11] (by building on the approach developed in [9,21]) the authors have obtained the quenched scalar-valued ASIP for certain classes of random piecewise expanding dynamics without any mixing assumptions for the base space. Finally, we mention two recent papers [33,34] by Su devoted to the ASIP for certain classes of random expanding maps and maps which admit a random tower extension. We note that while the latter two papers concern random dynamics with sub-exponential decay of correlations, the ASIP rates obtained there are not as good as the ones in [11] and the present paper.…”