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arXiv · 2202.02048

Differentiability of the diffusion coefficient for a family of intermittent maps

Fanni M. Sélley
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Abstract

It is well known that the Liverani-Saussol-Vaienti map satisfies a central limit theorem for H\"older observables in the parameter regime where the correlations are summable. We show that when $C^2$ observables are considered, the variance of the limiting normal distribution is a $C^1$ 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.

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Fanni M. Sélley. 2022-02-04. Differentiability of the diffusion coefficient for a family of intermittent maps. https://arxiv.org/abs/2202.02048

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