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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Shape convergence for aggregate tiles in conformal tilings
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by R. Kenyon and K. Stephenson PDF
Proc. Amer. Math. Soc. 147 (2019), 4275-4287 Request permission


Given a polygonal substitution tiling $T$ of the plane with subdivision rule $\tau$, we study the conformal tilings $T_n$ associated with $\tau ^nT$. We prove, under the assumption that there is somewhere a non-real similarity mapping one tile to another, that aggregate tiles within $T_n$ converge in shape as $n\rightarrow \infty$ to their associated Euclidean tiles in $T$.
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Additional Information
  • R. Kenyon
  • Affiliation: Department of Mathematics, Brown University, Providence, Rhode Island 02912
  • MR Author ID: 307971
  • Email:
  • K. Stephenson
  • Affiliation: Department of Mathematics, University of Tennessee, Knoxville, Tennessee 37996
  • MR Author ID: 216579
  • Email:
  • Received by editor(s): March 16, 2017
  • Received by editor(s) in revised form: October 30, 2017, and October 22, 2018
  • Published electronically: June 27, 2019
  • Additional Notes: Research of the first author was supported by NSF grants DMS-1612668, DMS-1713033 and the Simons Foundation award 327929.
    Research of the second author was supported by Simons Foundation award 208523.
  • Communicated by: Ken Bromberg
  • © Copyright 2019 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 147 (2019), 4275-4287
  • MSC (2010): Primary 37F30; Secondary 05B45
  • DOI:
  • MathSciNet review: 4002541