Rapid Convergence to Frequency for Substitution Tilings of the Plane

José Aliste-Prieto; Daniel Coronel; Jean Marc Gambaudo

doi:10.1007/s00220-011-1274-1

Rapid Convergence to Frequency for Substitution Tilings of the Plane

José Aliste-Prieto, Daniel Coronel, Jean Marc Gambaudo

Exact Sciences School

Research output: Contribution to journal › Article › peer-review

8 Citations (Scopus)

Abstract

This paper concerns self-similar tilings of the Euclidean plane. 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 many well-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.

Original language	English
Pages (from-to)	365-380
Number of pages	16
Journal	Communications in Mathematical Physics
Volume	306
Issue number	2
DOIs	https://doi.org/10.1007/s00220-011-1274-1
Publication status	Published - Sept 2011

ASJC Scopus subject areas

Statistical and Nonlinear Physics
Mathematical Physics

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10.1007/s00220-011-1274-1

Cite this

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abstract = "This paper concerns self-similar tilings of the Euclidean plane. 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 many well-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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AB - This paper concerns self-similar tilings of the Euclidean plane. 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 many well-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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Rapid Convergence to Frequency for Substitution Tilings of the Plane

Abstract

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