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arXiv:math/0306216 [math.PR]AbstractReferencesReviewsResources

The arctic circle boundary and the Airy process

Kurt Johansson

Published 2003-06-13, updated 2005-04-06Version 3

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.

Comments: 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)
Journal: Annals of Probability 2005, Vol. 33, No. 1, 1-30
Categories: math.PR, math-ph, math.MP
Subjects: 60K35, 82B20, 15A52
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