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

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