Quenched Invariance Principle for the Random Walk on the Penrose Tiling
Probability
2014-07-08 v3
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
Cite
@article{arxiv.1311.7023,
title = {Quenched Invariance Principle for the Random Walk on the Penrose Tiling},
author = {Zs. Bartha and A. Telcs},
journal= {arXiv preprint arXiv:1311.7023},
year = {2014}
}
Comments
15 pages, 1 figure