Conformal invariance of domino tiling
Conformal invariance of domino tiling
复制标题
DOI：
10.1214/aop/1019160260
复制
发表时间：
2000-04-01
影响因子：
2.3
通讯作者：
Kenyon, R
中科院分区：
文献类型：
--
作者：
Kenyon, R
设U是R-2中一个边界光滑的多连通区域。设P-Z是ε Z（2）中的一个多项式，U近似为ε-> 0。我们证明了，对于P-U上的某些边界条件，P-U的随机多米诺平铺（二聚体覆盖）上的高度分布在当U趋于0时的极限上是共形不变的，在这个意义上，边界分量的高度分布（或者更确切地说，与它们的平均值的高度差）只取决于U的共形类型.平均高度不是严格共形不变的，而是在共形映射下以一种简单的方式进行解析变换。明确评估平均高度和所有力矩。
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.