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Rapid Convergence to Frequency for Substitution Tilings of the Plane

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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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Authors and Affiliations

  1. Centro de Modelamiento Matemático, Universidad de Chile, Blanco Encalada 2120 7to. piso, Santiago, Chile

    José Aliste-Prieto

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Campus San Joaquín, Avenida Vicuña Mackenna 4860, Santiago, Chile

    Daniel Coronel

  3. Laboratoire J.-A. Dieudonné, Université de Nice - Sophia Antipolis, CNRS, 06108, Nice Cedex 02, France

    Jean-Marc Gambaudo

Authors
  1. José Aliste-Prieto
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  2. Daniel Coronel
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  3. Jean-Marc Gambaudo
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Correspondence to Jean-Marc Gambaudo.

Additional information

Communicated by G. Gallavotti

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Aliste-Prieto, J., Coronel, D. & Gambaudo, JM. Rapid Convergence to Frequency for Substitution Tilings of the Plane. Commun. Math. Phys. 306, 365–380 (2011). https://doi.org/10.1007/s00220-011-1274-1

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  • DOI: https://doi.org/10.1007/s00220-011-1274-1

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