论文标题
限制签约两分图的完美匹配形状
Limit shape of perfect matchings on contracting bipartite graphs
论文作者
论文摘要
我们考虑将某些边缘的重量定期为0，以使某些边缘重量为0，以周期性的方式考虑在一般的合同二分图上的随机完美匹配。我们在缩放限制中获得确定性极限形状。该结果还可以应用于证明所有具有一定边缘权重的合同方形晶格的多个断开液体区域的存在，从[13]中扩展了在[13]中证明的结果，用于收缩平方 - 赫克萨图晶格，其中每个周期中的平方行数为0或1。
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.
