Conformal invariance of domino tiling
成果类型：
Article
署名作者：
Kenyon, R
署名单位：
Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Universite Paris Saclay
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1019160260
发表日期：
2000
页码：
759-795
关键词：
摘要：
Let U be a multiply connected region in R-2 with smooth boundary. Let P-epsilon be a polyomino in epsilonZ(2) approximating U as epsilon --> 0. We show that, for certain boundary conditions on P-epsilon, the height distribution on a random domino tiling (dimer covering) of P-epsilon is conformally invariant in the limit as epsilon tends to 0, in the sense that the distribution of heights of boundary components (or rather, the difference of the heights from their mean values) only depends on the conformal type of U. The mean height is not strictly conformally invariant but transforms analytically under conformal mappings in a simple way. The mean height and all the moments are explicitly evaluated.