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The arctic circle boundary and the Airy process

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arxiv math/0306216 v3 pith:VGZPGI4A submitted 2003-06-13 math.PR math-phmath.MP

Kurt Johansson This is my paper · ORCID
classification math.PRmath-phmath.MP
keywords airyaztecboundarydiamondprocessproveappropriatelyarctic
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We prove that the, appropriately rescaled, boundary of the north polar region in the Aztec diamond converges to the Airy process. The proof uses certain determinantal point processes given by the extended Krawtchouk kernel. We also prove a version of Propp's conjecture concerning the structure of the tiling at the center of the Aztec diamond.

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  1. Domino Tilings of the Aztec Diamond in Random Environment and Schur Generating Functions

    math.PR 2025-07 conditional novelty 7.0 of 10

    For Aztec diamond tilings with i.i.d. one-periodic edge weights, height function fluctuations are, in the critical regime, GFF plus independent Brownian motion, and in the fixed-variance regime, Brownian motion alone ...

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