双二聚体模型中的连接概率--两种连接模式的情况
Connection probabilities in the double-dimer model -- the case of two connectivity patterns
摘要：
我们应用格拉斯曼表示的二聚体模型，一个等价的方法Kasteleyn的解决方案的紧密堆积的二聚体问题，计算连接概率的双二聚体模型有线/免费/有线/免费的边界条件，在一个矩形子域的正方形格子与四个标记的边界点的角落。利用与Schwarz-Christoffel变换有关的级数恒等式，我们证明了结果的连续性与上半平面中相应的连续性是一致的（先前由Kenyon-Wilson获得），其又与从边界发出的4SLE $_4$的连接概率相同，或者等效地，在共形回路系综的背景下，将CLE $_4$转换为具有有线/自由/有线/自由边界条件的条件版本。
英文摘要：
We apply the Grassmannian representation of the dimer model, an equivalent approach to Kasteleyn's solution to the close-packed dimer problem, to calculate the connection probabilities for the double-dimer model with wired/free/wired/free boundary conditions, on a rectangular subdomain of the square lattice with four marked boundary points at the corners. Using some series identities related to Schwarz-Christoffel transformations, we show that the continuum of the result is consistent with the corresponding one in the upper half-plane (previously obtained by Kenyon-Wilson), which is in turn identical to the connection probabilities for 4SLE$_4$ emanating from the boundary, or equivalently, to a conditioned version of CLE$_4$ with wired/free/wired/free boundary conditions in the context of conformal loop ensembles.
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