论文标题
在半线上完全不对称的一维布尔渗透模型中的非平凡性
Non-triviality in a totally asymmetric one-dimensional Boolean percolation model on a half-line
论文作者
论文摘要
众所周知，标准的一维布尔渗透模型中有两个制度：整个空间都覆盖了A.S.，或者覆盖的体积分数严格少于一个。这项工作的目的是证明，在半线上完全不对称晶粒的布尔模型中有第三种可能性：A.S。没有无限的组件，但是覆盖的体积分数是一个。给出了一个明确的条件，以表征存在无限的占领组件的存在。
It is well known that there are two regimes in a standard one-dimensional Boolean percolation model: either the entire space is covered a.s., or the covered volume fraction is strictly less than one. The aim of this work is to demonstrate that there is a third possibility in a Boolean model with totally asymmetric grains on a half-line: a.s. there is no unbounded component, but the covered volume fraction is one. An explicit condition is given characterizing the existence of an unbounded occupied component.
