论文标题
概率的细胞自动机，该自动机无法获得成功的基础I.I.D.耦合
A probabilistic cellular automaton that admits no successful basic i.i.d. coupling
论文作者
论文摘要
在本文中，我们重新审视了{0，1} z上概率细胞自动机（PCA）的经典示例，即，左右近额外细胞状态的加法2，然后保留加法的结果，具有概率p，或用概率为1- p。众所周知，对于$] 0，1的任何值的p $ \ [，该pca都是ergodic。我们表明，对于足够接近1的P，没有基于I.I.D的组成的PCA动力学耦合。最接近的纽布状态的随机函数（我们将其称为基本的I.I.D.耦合）可以成功，在此成功意味着，对于任何给定的单元，对于任何给定的单元，每个可能的初始条件都会在T时间步骤后导致同一状态，而在T时间步骤后，T to t to t to Infinity to Infinity。特别是，这排除了基于这种耦合的CFTP方案的可能性。该属性与单调PCA的情况形成鲜明对比，一旦成立，就会有一个成功的基本I.I.D.耦合。
In this paper, we revisit a classic example of probabilistic cellular automaton (PCA) on {0, 1} Z , namely, addition modulo 2 of the states of the left-and right-neighbouring cells, followed by either preserving the result of the addition, with probability p, or flipping it, with probability 1 -- p. It is well-known that, for any value of p $\in$]0, 1[, this PCA is ergodic. We show that, for p sufficiently close to 1, no coupling of the PCA dynamics based on the composition of i.i.d. random functions of nearest-neighbour states (we call this a basic i.i.d. coupling), can be successful, where successful means that, for any given cell, the probability that every possible initial condition leads to the same state after t time steps, goes to 1 as t goes to infinity. In particular, this precludes the possibility of a CFTP scheme being based on such a coupling. This property stands in sharp contrast with the case of monotone PCA, for which, as soon as ergodicity holds, there exists a successful basic i.i.d. coupling.
