Quenched Invariance Principle for the Random Walk on the Penrose Tiling

Zs. Bartha, A. Telcs

2014, v.20, №4, 751-767

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.

Keywords: random walk,random media,Penrose tiling,quenched invarianceprinciple,corrector method

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