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Lozenge Tilings of Hexagons with Cuts and Asymptotic Fluctuations: a New Universality Class

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Abstract

This paper investigates lozenge tilings of non-convex hexagonal regions and more specifically the asymptotic fluctuations of the tilings within and near the strip formed by opposite cuts in the regions, when the size of the regions tend to infinity, together with the cuts. It leads to a new kernel, which is expected to have universality properties.

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Author information

Authors and Affiliations

  1. Department of Mathematics, Brandeis University, Waltham, MA, 02453, USA

    Mark Adler & Pierre van Moerbeke

  2. Department of Mathematics, KTH Royal Institute of Technology, Stockholm, Sweden

    Kurt Johansson

  3. Department of Mathematics, Université de Louvain, 1348, Louvain-la-Neuve, Belgium

    Pierre van Moerbeke

Authors
  1. Mark Adler
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  2. Kurt Johansson
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  3. Pierre van Moerbeke
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Corresponding author

Correspondence to Mark Adler.

Additional information

The support of a Simons Foundation Grant # 278931 is gratefully acknowledged. M.A. thanks the Simons Center for Geometry and Physics for its hospitality.

The support of the Swedish Research Council (VR) and grant KAW 2010.0063 of the Knut and Alice Wallenberg Foundation are gratefully acknowledged.

The support of a Simons Foundation Grant # 280945 is gratefully acknowledged. PvM thanks the Simons Center for Geometry and Physics, Stony Brook, and the Kavli Institute of Physics, Santa Barbara, for their hospitality.

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Adler, M., Johansson, K. & van Moerbeke, P. Lozenge Tilings of Hexagons with Cuts and Asymptotic Fluctuations: a New Universality Class. Math Phys Anal Geom 21, 9 (2018). https://doi.org/10.1007/s11040-018-9265-5

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  • DOI: https://doi.org/10.1007/s11040-018-9265-5

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