Percolation and isoperimetry on roughly transitive graphs
Percolation and isoperimetry on roughly transitive graphs
复制标题
粗略传递图上的渗流和等周测量
DOI：
10.1214/17-aihp857
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. Teixeira
中科院分区：
文献类型：
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作者：
Elisabetta Candellero;A. Teixeira
本文研究了具有多项式增长且等周维数大于1的粗传递图G的渗流问题。对于这些图，我们能够证明p_c < 1，或者换句话说，存在一个渗流相。文章的主要结果的依赖和独立的渗流过程的工作，因为它们是基于一个相当强大的重整化技术。当G是可迁的时，p_c < 1是已知的.但即使在这种情况下，我们的证明产生了一些新的结果，它是完全概率的，不涉及使用格罗莫夫定理的群体的多项式增长。最后，我们给出了相关渗流的一些例子，我们的结果适用。
In this paper we study percolation on a roughly transitive graph G with polynomial growth and isoperimetric dimension larger than one. For these graphs we are able to prove that p_c < 1, or in other words, that there exists a percolation phase. The main results of the article work for both dependent and independent percolation processes, since they are based on a quite robust renormalization technique. When G is transitive, the fact that p_c < 1 was already known before. But even in that case our proof yields some new results and it is entirely probabilistic, not involving the use of Gromov's theorem on groups of polynomial growth. We finish the paper giving some examples of dependent percolation for which our results apply.