The arctic circle boundary and the Airy process
概率论
2017-11-22 v3 数学物理
math.MP
摘要
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.
引用
@article{arxiv.math/0306216,
title = {The arctic circle boundary and the Airy process},
author = {Kurt Johansson},
journal= {arXiv preprint arXiv:math/0306216},
year = {2017}
}
备注
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)