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 of th...

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Bibliographic Details
Published in:The Annals of Probability
Main Author: Johansson, Kurt
Format: Text
Language:English
Published: The Institute of Mathematical Statistics 2005
Subjects:
Airy process
determinantal process
Dimer model
random matrices
random tiling
60K35
82B20
15A52
Arctic
Online Access:https://projecteuclid.org/euclid.aop/1108141718
https://doi.org/10.1214/009117904000000937
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.

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