Decay of correlations and limit theorems for random intermittent maps

TL;DR

This paper investigates the decay of correlations and limit theorems for random intermittent maps, establishing conditions for polynomial memory loss, central limit theorems, and invariance principles in a stochastic setting.

Contribution

It introduces new results on quenched decay of correlations and limit theorems for random LSV maps with less restrictive conditions on the parameter beta.

Findings

Proves polynomial decay of correlations for random LSV maps.

Establishes central limit theorems with explicit rates.

Demonstrates almost sure invariance principles under certain conditions.

Abstract

In this paper, we revisit the problem of polynomial memory loss and the central limit theorem for time-dependent LSV maps. More precisely, we show that for random LSV maps corresponding to a random parameter beta() we obtain quenched memory loss, decay of correlations, central limit theorems with rates, moment bounds and almost sure invariance principles (ASIP) when the essential infimum of beta() is less than 1/5 and the driving process (i.e. random environment) is mixing sufficiently fast. In [59, Corollary 3.8] the ASIP was obtained for ergodic driving systems when the essential supremum of \b{eta} is less than 1/2. 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