The arctic circle boundary and the Airy process
Probability
2017-11-22 v3 Mathematical Physics
math.MP
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.
Cite
@article{arxiv.math/0306216,
title = {The arctic circle boundary and the Airy process},
author = {Kurt Johansson},
journal= {arXiv preprint arXiv:math/0306216},
year = {2017}
}
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)