Rafael de la Llave, Alistair Windsor
Published 2008-09-08Version 1
We show that given any tiling of Euclidean space, any geometric patterns of points, we can find a patch of tiles (of arbitrarily large size) so that copies of this patch appear in the tiling nearly centered on a scaled and translated version of the pattern. The rather simple proof uses Furstenberg's topological multiple recurrence theorem.
Metrics on tiling spaces, local isomorphism and an application of Brown's Lemma
On non-Archimedean recurrence equations and their applications
A non-varying phenomenon with an application to the wind-tree model
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