Large deviations and central limit theorems for sequential and random systems of intermittent maps

TL;DR

This paper establishes large deviations estimates and quenched central limit theorems for sequential and random compositions of intermittent maps, extending previous results by enlarging parameter ranges and clarifying the role of centering.

Contribution

It extends quenched CLT results for intermittent maps by broadening parameter ranges and demonstrating the necessity of centering for the CLT.

Findings

Large deviations estimates for intermittent maps.

Extended quenched CLT to wider parameter ranges.

Proved variance is almost surely constant and equal to the annealed variance.

Abstract

We obtain large deviations estimates for both sequential and random compositions of intermittent maps. We also address the question of whether or not centering is necessary for the quenched central limit theorems (CLT) obtained by Nicol, T\"or\"ok and Vaienti for random dynamical systems comprised of intermittent maps. Using recent work of Abdelkader and Aimino, Hella and Stenlund we extend the results of Nicol, T\"or\"ok and Vaienti on quenched central limit theorems (CLT) for centered observables over random compositions of intermittent maps: first by enlarging the parameter range over which the quenched CLT holds; and second by showing that the variance in the quenched CLT is almost surely constant (and the same as the variance of the annealed CLT) and that centering is needed to obtain this quenched CLT.