等径二聚体模型的共形不变性&三角形四分块情形
Conformal invariance of isoradial dimer models & the case of triangular quadri-tilings
摘要：
我们考虑二聚体模型的图是二分的，周期性的，并满足一个几何条件称为{ \em isoradiality}，定义在\cite{Kenyon3}。我们表明，任何这样的二聚体模型的高度函数的标度极限是$1/\sqrtπ$倍的高斯自由场。三角四边形镶嵌是在\cite{Bea}中引入的，它们是由菱形镶嵌产生的一类等径图上的二聚体模型。通过两个高度函数，它们可以被解释为2+2维的随机界面。我们证明了两个高度函数的标度极限都是$1/\sqrtπ$乘以一个高斯自由场，并且这两个高斯自由场是独立的。
英文摘要：
We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called {\em isoradiality}, defined in \cite{Kenyon3}. We show that the scaling limit of the height function of any such dimer model is $1/\sqrtπ$ times a Gaussian free field. Triangular quadri-tilings were introduced in \cite{Bea}; they are dimer models on a family of isoradial graphs arising form rhombus tilings. By means of two height functions, they can be interpreted as random interfaces in dimension 2+2. We show that the scaling limit of each of the two height functions is $1/\sqrtπ$ times a Gaussian free field, and that the two Gaussian free fields are independent.
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