The arctic circle boundary and the Airy process

Details The arctic circle boundary and the Airy process The arctic circle boundary and the Airy process

2003-06-13

arxiv.org/abs/math/0306216v3

Annals of Probability 2005, Vol. 33, No. 1, 1-30

Mathematics

Probability

Published at http://dx.doi.org/10.1214/009117904000000937 in the Annals of Probability (http://www.imstat.org/aop/) by the Ins

Scientific paper

10.1214/009117904000000937

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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