Comment on "Lyapunov statistics and mixing rates for intermittent systems"

TL;DR

This paper critically examines claims about the relationship between correlation decay and large deviations in intermittent maps, providing rigorous arguments and estimates to clarify the issue and counter objections in prior work.

Contribution

It offers a rigorous analysis and analytic estimates that disprove previous objections regarding correlation decay and large deviations in ergodic intermittent systems.

Findings

Disproves objections raised in prior work about correlation decay.

Provides rigorous arguments and analytic estimates.

Clarifies the relationship between correlation decay and large deviations.

Abstract

In Pires {\it et al.} [Phys. Rev. E 84, 066210 (2011)] intermittent maps are considered, and the tight relationship between correlation decay of smooth observables and large deviations estimates, as for instance employed in Artuso and Manchein [Phys. Rev. E 80, 036210 (2009)], is questioned. We try to clarify the problem, and provide rigorous arguments and an analytic estimate that disprove the objections raised in Pires {\it et al.} [Phys. Rev. E 84, 066210 (2011)] when ergodic systems are considered.