Invariant Measures and Convergence for Cellular Automaton 184 and Related Processes

A non-ergodic probabilistic cellular automaton with a unique invariant measure

We exhibit a Probabilistic Cellular Automaton (PCA) on the integers with an alphabet and a neighborhood of size 2 which is non-ergodic although it has a unique invariant measure. This answers by the negative an old open question on whether uniqueness of the invariant measure implies ergodicity for a PCA.

一个具有两种遍历性相变的扰动元胞自动机

A perturbed cellular automaton with two phase transitions for the ergodicity

本文利用Gács结果构造了一个具有两种遍历性相变的元胞自动机，证明其在小噪声速率下遍历、中等速率下非遍历、接近1的速率下再次遍历。

Transfer matrix analysis of one-dimensional majority cellular automata with thermal noise

Thermal noise in a cellular automaton refers to a random perturbation to its function which eventually leads this automaton to an equilibrium state controlled by a temperature parameter. We study the 1-dimensional majority-3 cellular automaton under this model of noise. Without noise, each cell in this automaton decides its next state by majority voting among itself and its left and right neighbour cells. Transfer matrix analysis shows that the automaton always reaches a state in which every cell is in one of its two states with probability 1/2 and thus cannot remember even one bit of informat…

基于二维马尔可夫链对具有 Margolus 邻域的元胞自动机中扩散的解析描述

Analytical description of the diffusion in a cellular automaton with the Margolus neighbourhood in terms of the two-dimensional Markov chain

本文通过引入辅助随机变量将具有 Margolus 邻域的二维元胞自动机单粒子运动归结为二维马尔可夫链，利用概率生成函数精确求解，并用 Jacobi 多项式表达概率分布，最终推导出扩散系数的精确解析公式。