On critical probabilities in percolation theory
On critical probabilities in percolation theory
复制标题
渗滤理论中的临界概率
DOI：
10.1063/1.523894
复制
发表时间：
1978
影响因子：
1.3
通讯作者：
J. Wierman
中科院分区：
文献类型：
--
作者：
J. Wierman
本文讨论了正方形格点上键渗流问题中临界渗流概率概念的几种不同形式。在证明两个新结果时，临界概率也被用作技术手段。首先，存在一个临界概率pT，低于该概率，簇大小的所有矩都是有限的。其次，一个无限连通开键簇以正概率存在当且仅当任意角扇区包含一个无限连通开键簇以正概率存在。导出了渗流模型中每个键的开团簇的预期数目的表达式，涉及到严格证明Sykes和Essam的临界概率结果的问题。
Several versions of the concept of critical percolation probability are discussed in the bond percolation problem on the square lattice. Critical probabilities are also employed as technical devices in the proofs of two new results. First, there is a critical probability pT below which all moments of the cluster size are finite. Secondly, an infinite connected cluster of open bonds exists with positive probability if and only if any angular sector contains an infinite connected cluster of open bonds with positive probability. An expression is derived for the expected number of open clusters per bond in the percolation model, relating to the problem of rigorously justifying a critical probability result of Sykes and Essam.