Decay of correlations and limit theorems for random intermittent maps

Abstract In this paper, we revisit the problem of polynomial memory loss and the central limit theorem (CLT) for time‐dependent LSV maps. More precisely, we show that for random LSV maps corresponding to a random parameter we obtain quenched memory loss, decay of correlations, CLTs with rates, moment bounds, and almost sure invariance principles (ASIPs) when the essential infimum of is sufficiently small and the driving process (i.e., random environment) is mixing sufficiently fast. Su obtained ASIP for ergodic driving systems when the essential supremum of is less than . As will be elaborated in Section 1, restrictions on the essential infimum are more natural in our context. Our results have an abstract form which we believe could be useful in other circumstances, as will be elaborated in a future work.