Quenched Invariance Principle for the Random Walk on the Penrose Tiling

Zs. Bartha, A. Telcs

Published 2013-11-27, updated 2014-07-05Version 3

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.