文章基本信息

标题：Indicable groups and $p_c<1$
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作者：Aran Raoufi ; Ariel Yadin
期刊名称：Electronic Communications in Probability
印刷版ISSN：1083-589X
出版年度：2017
卷号：22
DOI：10.1214/16-ECP40
语种：English
出版社：Electronic Communications in Probability
摘要：A conjecture of Benjamini & Schramm from 1996 states that any finitely generated group that is not a finite extension of $\mathbb{Z} $ has a non-trivial percolation phase. Our main results prove this conjecture for certain groups, and in particular prove that any group with a non-trivial homomorphism into the additive group of real numbers satisfies the conjecture. We use this to reduce the conjecture to the case of hereditary just-infinite groups.