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We consider the simple random walk on the graph corresponding to a Penrosetiling. We prove that the path distribution of the walk converges weakly tothat of a non-degenerate Brownian motion for almost every Penrose tiling withrespect to the appropriate invariant measure on the set of tilings. Our toolfor this is the corrector method.

Quenched Invariance Principle for the Random Walk on the Penrose Tiling