Almost sure mixing rates for non-uniformly expanding maps

Abstract

We consider random perturbations of non-uniformly expanding maps, possibly having a non-degenerate critical set. We prove that if the volume measure of the set of points failing the non-uniform expansion or the slow recurrence to the critical set, at a certain times has a (stretched) exponential decay for almost all random orbits, then the decay of correlations along random orbits is stretched exponential, up to some waiting time. As applications we obtain almost sure stretched exponential decay of correlations along random orbits for Viana maps, as for a class of non-uniformly expanding local diffeomorphisms and a family of unimodal maps.