收缩二部图上完美匹配的极限形状
Limit shape of perfect matchings on contracting bipartite graphs
摘要：
在收缩的正方形-六边形格上，通过周期性地使某些边权为0，研究了一类收缩的二部图上的随机完美匹配。我们得到了确定性的极限形状的标度极限。这些结果也可用于证明所有具有一定边权的收缩正方形-六边形格子都存在多个不连通液体区域，推广了[13]中证明的每个周期的正方形行数为0或1的收缩正方形-六边形格子的结果.
英文摘要：
We consider random perfect matchings on a general class of contracting bipartite graphs by letting certain edge weights be 0 on the contracting square-hexagon lattice in a periodic way. We obtain a deterministic limit shape in the scaling limit. The results can also be applied to prove the existence of multiple disconnected liquid regions for all the contracting square-hexagon lattices with certain edge weights, extending the results proved in [13] for contracting square-hexagon lattices where the number of square rows in each period is either 0 or 1.
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