Critical density of activated random walks on transitive graphs
Critical density of activated random walks on transitive graphs
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传递图上激活随机游走的临界密度
作者：
Alexandre O. Stauffer;L. Taggi
研究了一般顶点传递图上的激活随机游走模型。该模型的一个核心问题是，持续活动的临界密度$mu_c$是否严格在0和1之间。已知$mu_c> $对$mathbb{Z}^d$, $dgeq 1$, $mu_c 0$对任何顶点可传递的可调节图，$mu_cin(0,1)$对规则树的任何睡眠率。
We consider the activated random walk model on general vertex-transitive graphs. A central question in this model is whether the critical density $mu_c$ for sustained activity is strictly between 0 and 1. It was known that $mu_c>0$ on $mathbb{Z}^d$, $dgeq 1$, and that $mu_c 0$ in any vertex-transitive amenable graph, and that $mu_cin(0,1)$ for any sleeping rate on regular trees.