ON MIXING RATES FOR RANDOM PERTURBATIONS

Abstract

This thesis focuses on decay of correlations for non-uniformly expanding maps with random perturbations. By using a coupling argument on Young tower, it was known that the type of decay of correlations is essentially determined by the tail of recurrence time. More precisely, decay of correlations and the tail of recurrence time have the same kind of decay in deterministic case. Baladi et al. proved that the stretched-exponential tail of the recurrence time induces stretched-exponential decay of correlations for non-uniformly expanding maps with random perturbations. In this thesis, we consider random perturbations of non-uniformly expanding maps with different types of the return time tails.