Quenched Invariance Principle for the Random Walk on the Penrose Tiling

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.

15 pages, 1 figure

References in corpus (1)

• Quenched invariance principle for simple random walk on percolation clusters