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Local Geometry of the rough-smooth interface in the two-periodic Aztec diamond

Abstract : Random tilings of the two-periodic Aztec diamond contain three macroscopic regions: frozen, where the tilings are deterministic; rough, where the correlations between dominoes decay polynomially; smooth, where the correlations between dominoes decay exponentially. In a previous paper, the authors found that a certain averaging of height function differences at the rough-smooth interface converged to the extended Airy kernel point process. In this paper, we augment the local geometrical picture at this interface by introducing well-defined lattice paths which are closely related to the level lines of the height function. We show, after suitable centering and rescaling, that a point process from these paths converge to the extended Airy kernel point process provided that the natural parameter associated to the two-periodic Aztec diamond is small enough.
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https://hal.archives-ouvertes.fr/hal-02572271
Contributor : Vincent Beffara <>
Submitted on : Wednesday, May 13, 2020 - 3:38:56 PM
Last modification on : Monday, May 18, 2020 - 9:29:15 AM

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  • HAL Id : hal-02572271, version 1
  • ARXIV : 2004.14068

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Vincent Beffara, Sunil Chhita, Kurt Johansson. Local Geometry of the rough-smooth interface in the two-periodic Aztec diamond. 2020. ⟨hal-02572271⟩

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