Differentiability of the Diffusion Coefficient for a Family of Intermittent Maps

Abstract

AbstractIt is well known that the Liverani–Saussol–Vaienti map satisfies a central limit theorem for Hölder observables in the parameter regime where the correlations are summable. We show that when C2 observables are considered, the variance of the limiting normal distribution is a C1 function of the parameter. We first show this for the first return map to the base of the second branch by studying the Green-Kubo formula, then conclude the result for the original map using Kac’s lemma and relying on linear response.