文章基本信息

标题：Percolation Beyond $Z^d$, Many Questions And a Few Answers
本地全文：下载
作者：Benjamini, Itai ; Schramm, Oded
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：1996
卷号：1
页码：71-82
DOI：10.1214/ECP.v1-978
出版社：Electronic Communications in Probability
摘要：A comprehensive study of percolation in a more general context than the usual $Z^d$ setting is proposed, with particular focus on Cayley graphs, almost transitive graphs, and planar graphs. Results concerning uniqueness of infinite clusters and inequalities for the critical value $p_c$ are given, and a simple planar example exhibiting uniqueness and non-uniqueness for different $p>p_c$ is analyzed. Numerous varied conjectures and problems are proposed, with the hope of setting goals for future research in percolation theory.
关键词：Percolation, criticality, planar graph, transitive graph, isoperimetericinequality;82B43, 60K35