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Partition function of periodic isoradial dimer models
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  • Published: 17 November 2006

Partition function of periodic isoradial dimer models

  • Béeatrice de Tilière1 

Probability Theory and Related Fields volume 138, pages 451–462 (2007)Cite this article

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Abstract

Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)—they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal partition function has a simple explicit formula involving the local geometry of the graph only. This is a surprising feature of periodic isoradial dimer models, which does not hold in the general periodic dimer case (Kenyon et al. in Ann Math, 2006).

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Authors and Affiliations

  1. Institut für Mathematik, Universität Zürich, Winterthurerstrasse 190, 8057, Zürich, Switzerland

    Béeatrice de Tilière

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  1. Béeatrice de Tilière
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Correspondence to Béeatrice de Tilière.

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Supported by Swiss National Fund under grant 47102009.

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de Tilière, B. Partition function of periodic isoradial dimer models. Probab. Theory Relat. Fields 138, 451–462 (2007). https://doi.org/10.1007/s00440-006-0041-2

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  • Received: 24 May 2006

  • Revised: 03 October 2006

  • Published: 17 November 2006

  • Issue Date: July 2007

  • DOI: https://doi.org/10.1007/s00440-006-0041-2

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Mathematics Subject Classification (2000)

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