LOCALITY OF PERCOLATION FOR ABELIAN CAYLEY GRAPHS
成果类型：
Article
署名作者：
Martineau, Sebastien; Tassion, Vincent
署名单位：
Weizmann Institute of Science; Swiss Federal Institutes of Technology Domain; ETH Zurich
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/15-AOP1086
发表日期：
2017
页码：
1247-1277
关键词：
摘要：
We prove that the value of the critical probability for percolation on an Abelian Cayley graph is determined by its local structure. This is a partial positive answer to a conjecture of Schramm: the function pc defined on the set of Cayley graphs of Abelian groups of rank at least 2 is continuous for the Benjamini-Schramm topology. The proof involves group-theoretic tools and a new block argument.