论文标题
具有基于奇偶校验的社区的广义概率细胞自动机的遗传性
Ergodicity of a generalized probabilistic cellular automaton with parity-based neighbourhoods
论文作者
论文摘要
我们研究了一个一维概率的概率蜂窝自动机$ e_ {p，q} $，带有宇宙$ \ mathbb z $，alphabet $ \ mathcal a = \ {0，1 \} $，参数$ \ MATHCAL N = \ {1，2 \} $。在$ e_ {p，q，q，q} $的任何$ x \ in \ e_ {p，q，q} $下的任何$ x \ in \ mathbb z $的状态$ e_ {p，q}η（x）$是一个随机变量，其概率分布取决于$η（x + y）$ for $ y \ for $ y \ in Mathcal n_i $ y $ i $ i $ a $ a $ a $ x $ as $ x $。我们通过在二维晶格上与合适的渗透游戏的连接来建立该GPCA的奇特性，用于$ p $和$ q $的各种范围。对于$ p $和$ q $的这些相同值的范围，我们表明上述游戏的概率为$ 0 $，从而导致平局。
We study a one-dimensional generalized probabilistic cellular automaton $E_{p, q}$ with universe $\mathbb Z$, alphabet $\mathcal A = \{0, 1\}$, parameters $p$ and $q$ such that $0 < p+q \leq 1$ and two neighbourhoods $\mathcal N_0 = \{0, 1\}$ and $\mathcal N = \{1, 2\}$. The state $E_{p, q} η(x)$ of any $x \in \mathbb Z$ under the application of $E_{p, q}$ is a random variable whose probability distribution depends on the states $η(x + y)$ for $y \in \mathcal N_i$ where $i$ has the same parity as $x$. We establish ergodicity of this GPCA for various ranges of values of $p$ and $q$ via its connection with a suitable percolation game on a two-dimensional lattice. For these same ranges of values of $p$ and $q$, we show that the above-mentioned game has probability $0$ of resulting in a draw.
