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arXiv · 1606.02470

Spectral measure at zero for self-similar tilings

Jordan Emme
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Abstract

The goal of this paper is to study the action of the group of translations over self-similar tilings in the euclidian space $\mathbb{R}^d$. It investigates the behaviour near zero for spectral measures for such dynamical systems. Namely the paper gives a H\"older asymptotic expansion near zero for these spectral measures. It is a generalization to higher dimension of a result by Bufetov and Solomyak who studied self similar-suspension flows for substitutions. The study of such asymptotics mostly involves the understanding of the deviations of some ergodic averages.

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Jordan Emme. 2016-06-08. Spectral measure at zero for self-similar tilings. https://arxiv.org/abs/1606.02470

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