Percolation on finite Cayley graphs

被引：2
|
作者：
Malon, Christopher [1 ]
Pak, Igor [1 ]
机构：
[1] MIT, Dept Math, Cambridge, MA 02139 USA
来源：
COMBINATORICS PROBABILITY & COMPUTING | 2006年 / 15卷 / 04期
关键词：
D O I：
10.1017/S0963548305007406
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we study percolation on finite Cayley graphs. A conjecture of Benjamini says that the critical percolation p(c) of any vertex-transitive graph satisfying a certain diameter condition can be bounded away from one. We prove Benjamini's conjecture for some special classes of Cayley graphs. We also establish a reduction theorem, which allows us to build Cayley graphs for large groups without increasing p(c).
引用
收藏
页码：571 / 588
页数：18
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