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arXiv · 1311.7023

Quenched Invariance Principle for the Random Walk on the Penrose Tiling

Zs. Bartha·A. Telcs
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Abstract

We consider the simple random walk on the graph corresponding to a Penrose tiling. We prove that the path distribution of the walk converges weakly to that of a non-degenerate Brownian motion for almost every Penrose tiling with respect to the appropriate invariant measure on the set of tilings. Our tool for this is the corrector method.

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BibTeXRIS

Zs. Bartha, A. Telcs. 2014-07-05. Quenched Invariance Principle for the Random Walk on the Penrose Tiling. https://arxiv.org/abs/1311.7023

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