论文标题
匹配晶格对的渗透临界概率
Percolation critical probabilities of matching lattice-pairs
论文作者
论文摘要
对于严格不平等的$ p_c（g _*）<p_c（g）$，建立了一个必要的条件，在Quasi-Transi-Transitive，Plane Graph $ g $上以及其匹配的图形$ g _*$之间的站点渗透的关键概率之间。假定$ g $正确地嵌入了欧几里得或双曲机平面中。当$ g $是传递的时，当$ g $不是三角剖分时，严格的不平等就会存在。 基本方法是增强功能的标准方法，但是其实现是由非欧国人（双曲线）空间，位点研究（而不是键）渗透的研究以及准转换假设的一般性而产生的。 该结果与作者（“双曲线站点渗透”，arxiv：2203.00981）的工作补充，在等价$ p_u（g） + p_c（g_*）= 1 $上，其中$ p_u $是存在独特的无限开放式群集的关键可能性。这意味着对于$ g $ $ p_u（g） + p_c（g）\ ge 1 $，当且仅当$ g $是三角剖分时，它具有平等。
A necessary and sufficient condition is established for the strict inequality $p_c(G_*)<p_c(G)$ between the critical probabilities of site percolation on a quasi-transitive, plane graph $G$ and on its matching graph $G_*$. It is assumed that $G$ is properly embedded in either the Euclidean or the hyperbolic plane. When $G$ is transitive, strict inequality holds if and only if $G$ is not a triangulation. The basic approach is the standard method of enhancements, but its implemention has complexity arising from the non-Euclidean (hyperbolic) space, the study of site (rather than bond) percolation, and the generality of the assumption of quasi-transitivity. This result is complementary to the work of the authors ("Hyperbolic site percolation", arXiv:2203.00981) on the equality $p_u(G) + p_c(G_*) = 1$, where $p_u$ is the critical probability for the existence of a unique infinite open cluster. It implies for transitive $G$ that $p_u(G) + p_c(G) \ge 1$, with equality if and only if $G$ is a triangulation.
