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The Arctic Circle Boundary and the Airy Process

Kurt Johansson
The Annals of Probability
Vol. 33, No. 1 (Jan., 2005), pp. 1-30
Stable URL: http://www.jstor.org/stable/3481761
Page Count: 30
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
The Arctic Circle Boundary and the Airy Process
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Abstract

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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