论文标题
通过Toom Contours渗透亚临界引导渗透
Subcritical bootstrap percolation via Toom contours
论文作者
论文摘要
在本说明中，我们提供了一个替代证明，即亚临界引导渗透模型在任何维度上具有积极的关键概率。证明依赖于Toom的古典框架的最新扩展。这种方法不仅比在两个且更大的维度中的原始多尺度重量法化证明更简单，而且给出了明显更好的界限。作为副产品，我们提高了Toom东北中心多数统治蜂窝自动机的稳定性阈值的最著名界限。
In this note we provide an alternative proof of the fact that subcritical bootstrap percolation models have a positive critical probability in any dimension. The proof relies on a recent extension of the classical framework of Toom. This approach is not only simpler than the original multi-scale renormalisation proof of the result in two and more dimensions, but also gives significantly better bounds. As a byproduct, we improve the best known bounds for the stability threshold of Toom's North-East-Center majority rule cellular automaton.
