标题： 具有两个相变的遍历性扰动细胞自动机 显示英文标题

标题： A perturbed cellular automaton with two phase transitions for the ergodicity

摘要： 正率猜想指出，具有严格正转移率的一维概率细胞自动机（PCA）必须是遍历的。 该猜想被Gács驳斥，他的反例是一个在足够小速率的均匀随机噪声下非遍历的细胞自动机。 对于所有已知的反例，非遍历性已在足够小的速率下得到证明。 相反，所有细胞自动机在足够高的噪声速率下都是遍历的。 目前尚未发现其他类型的遍历性相变，且已知反例在中间噪声速率下的行为尚不清楚。 我们提出一个具有两个相变的细胞自动机的例子。 利用Gács的结果作为一个黑箱，我们构造了一个在小噪声速率下是遍历的，在稍高速率下是非遍历的，并且在接近1的速率下再次是遍历的细胞自动机。 显示英文摘要

摘要： The positive rates conjecture states that a one-dimensional probabilistic cellular automaton (PCA) with strictly positive transition rates must be ergodic. The conjecture has been refuted by G\'acs, whose counterexample is a cellular automaton that is non-ergodic under uniform random noise with sufficiently small rate. For all known counterexamples, non-ergodicity has been proved under small enough rates. Conversely, all cellular automata are ergodic with sufficiently high-rate noise. No other types of phase transitions of ergodicity are known, and the behavior of known counterexamples under intermediate noise rates is unknown. We present an example of a cellular automaton with two phase transitions. Using G\'acs's result as a black box, we construct a cellular automaton that is ergodic under small noise rates, non-ergodic for slightly higher rates, and again ergodic for rates close to 1.