带孔随机平铺结构中静电场作为费曼和的出现
The emergence of the electrostatic field as a Feynman sum in random tilings with holes
摘要：
我们考虑三角形格子上的随机菱形镶嵌，其中孔$Q_1,...,Q_n$在某个固定的位置。对于每个单位三角形不是在一个洞，考虑的菱形覆盖it.We的平均取向表明，这个离散场的缩放限制是静电场时，得到的每个孔$Q_i$作为一个电荷的大小等于两个不同的取向内$Q_i$的单位三角形的数量之间的差异。然后，这是重述的随机表面，产生的结果是，平均超过表面与规定的高度在工会的边界的孔，在缩放限制，螺旋面的总和。
英文摘要：
We consider random lozenge tilings on the triangular lattice with holes $Q_1,...,Q_n$ in some fixed position. For each unit triangle not in a hole, consider the average orientation of the lozenge covering it. We show that the scaling limit of this discrete field is the electrostatic field obtained when regarding each hole $Q_i$ as an electrical charge of magnitude equal to the difference between the number of unit triangles of the two different orientations inside $Q_i$. This is then restated in terms of random surfaces, yielding the result that the average over surfaces with prescribed height at the union of the boundaries of the holes is, in the scaling limit, a sum of helicoids.
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