The arctic circle boundary and the Airy process

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...

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Bibliographic Details
Main Author: Johansson, Kurt
Format: Text
Language:unknown
Published: arXiv 2003
Subjects:
Probability math.PR
Mathematical Physics math-ph
FOS Mathematics
FOS Physical sciences
60K35 Primary 82B20, 15A52. Secondary
Arctic
Online Access:https://dx.doi.org/10.48550/arxiv.math/0306216
https://arxiv.org/abs/math/0306216
Description
Summary: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. : Published at http://dx.doi.org/10.1214/009117904000000937 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org)

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