论文标题
在一类概率的蜂窝蜂窝自动机上，尺寸为-3美元及其在渗透游戏中的应用
On a class of probabilistic cellular automata with size-$3$ neighbourhood and their applications in percolation games
论文作者
论文摘要
$ \ Mathbb {z}^{2} $上的不同版本的渗透游戏，带有参数$ p $和$ q $，分别指示了$ \ mathbb {z}^{2} $ in a trap的可能性和$ p prog的可能性，$ pr的可能性+p+pr+p+p+p+p+p+p+p+p+p+p+p+p++ 0 $。我们表明，对于固定的$ p $和$ q $，在这些游戏中的每一个绘制的可能性为$ 0 $，并且仅当某个$ 1 $ dimensional概率的概率的蜂窝式自动机（PCA）$ f_ {p，q，q} $带有size-$ 3 $ nekool的邻居。这使我们能够得出结论，每当$ p+q> 0 $时，$ f_ {p，q} $都是ergodic，从而严格地建立了相当一类的PCAS的Ergodicity。
Different versions of percolation games on $\mathbb{Z}^{2}$, with parameters $p$ and $q$ that indicate, respectively, the probability with which a site in $\mathbb{Z}^{2}$ is labeled a trap and the probability with which it is labeled a target, are shown to have probability $0$ of culminating in draws when $p+q > 0$. We show that, for fixed $p$ and $q$, the probability of draw in each of these games is $0$ if and only if a certain $1$-dimensional probabilistic cellular automaton (PCA) $F_{p,q}$ with a size-$3$ neighbourhood is ergodic. This allows us to conclude that $F_{p,q}$ is ergodic whenever $p+q > 0$, thereby rigorously establishing ergodicity for a considerable class of PCAs.
