Stationary measures and phase transition for a class of probabilistic cellular automata

自举渗流、概率元胞自动机与锐利性

Bootstrap percolation, probabilistic cellular automata and sharpness

本文通过建立渗流、自举渗流与概率及确定性元胞自动机之间的新联系，证明了吸引吸收型概率元胞自动机等模型相变的锐利性，并恢复和推广了 Toom 关于噪声稳定性的经典结果。

Coupling from the past for exponentially ergodic one-dimensional probabilistic cellular automata

We prove that, for every one-dimendional exponentially ergodic probabilistic cellular automaton with positive rates, there exists a locally defined coupling-from-the-past flow whose coalescence time has a finite exponential moment.

元胞自动机的强随机稳定性

Strong stochastic stability of cellular automata

本文针对受随机噪声扰动的元胞自动机，提出强随机稳定性概念，并通过图灵不可判定性证明该稳定性概念具有非平凡的理论意义。

Subcritical monotone cellular automata

We study monotone cellular automata (also known as $\mathcal{U}$-bootstrap percolation) in $\mathbb{Z}^d$ with random initial configurations. Confirming a conjecture of Balister, Bollobás, Przykucki and Smith, who proved the corresponding result in two dimensions, we show that the critical probability is non-zero for all subcritical models.

Right-Permutative Cellular Automata on Topological Markov Chains

In this paper we consider cellular automata $(\mathfrak{G},Φ)$ with algebraic local rules and such that $\mathfrak{G}$ is a topological Markov chain which has a structure compatible to this local rule. We characterize such cellular automata and study the convergence of the Cesàro mean distribution of the iterates of any probability measure with complete connections and summable decay.