Quenched Invariance Principle for the Random Walk on the Penrose Tiling

Bartha, Zsolt and Telcs, András (2014) Quenched Invariance Principle for the Random Walk on the Penrose Tiling. MARKOV PROCESSES AND RELATED FIELDS, 20 (4). pp. 751-767. ISSN 1024-2953

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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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