arXiv 1007.30142010-07math-phmath.DSmath.MP

Rapid convergence to frequency for Substitution Tilings of the Plane

J. Aliste-Prieto, D. Coronel, J. -M. Gambaudo

备注：: Minor corrections suggested by the referee. To appear in Communications in Mathematical Physics
DOI：: 10.1007/s00220-011-1274-1

英文摘要：

This paper concerns self-similar tilings in dimension 2. We consider the number of occurrences of a given tile in any domain bounded by a Jordan curve. For a large class of self-similar tilings, including most known examples, we give estimates of the oscillation of this number of occurrences around its average frequency times the total number of tiles in the domain, which depend only on the Jordan curve.

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