论文标题
在总重量退出有限的总重量上，在$ \ mathbb {z} $上的Shift-Invariant加权定向图中进行了牢固连接的集合
On total weight exiting finite, strongly connected sets in shift-invariant weighted directed graphs on $\mathbb{Z}$
论文作者
论文摘要
对于带有顶点套装$ \ mathbb {z} $的转移不变的加权定向图，我们检查了最小的权重$κ__0$退出有限的，紧密连接的顶点。尽管$κ__0$定义为immimum，但已证明始终由一组实际的顶点来实现。我们表明，对于每个基础有向图（在重量分配之前），有一个$κ_0$的公式，即边缘权重的最少有限的整数组合。我们为几个不同的有向图找到了此公式。这个问题的动机来自在迪利奇环境中的随机步行（等效地，边缘加强随机步行），其中已显示$κ_0$的大小可以确定有限陷阱的强度，在这种情况下，步行可以长时间被卡住。
For a shift-invariant weighted directed graph with vertex set $\mathbb{Z}$, we examine the minimal weight $κ_0$ exiting a finite, strongly connected set of vertices. Although $κ_0$ is defined as an infimum, it has been shown that the infimum is always attained by an actual set of vertices. We show that for each underlying directed graph (prior to assignment of the weights), there is a formula for $κ_0$ as a minimum of finitely many integer combinations of the edge weights. We find this formula for several different directed graphs. Motivation for this problem comes from random walks in Dirichlet environments (equivalently, directed edge reinforced random walks), where the size of $κ_0$ has been shown to determine the strength of finite traps where the walk can get stuck for a long time.
