Increasing coupling of probabilistic cellular automata

Abstract

We give a necessary and sufficient condition for the existence of an increasing coupling of $N$ ($N\ge 2$) synchronous dynamics on $S^{{\mathbb{Z}}^d}$(PCA). Increasing means the coupling preserves stochastic ordering. We first present our main construction theorem in the case where $S$ is totally ordered, applications to attractive PCA's are given. When $S$ is only partially ordered, we show on two examples that a coupling of more than two synchronous dynamics may not exist. We also prove an extension of our main result for a particular class of partially ordered spaces.

References in corpus (2)

• Stationary measures and phase transition for a class of probabilistic cellular automata
• Ergodicity of PCA: Equivalence between Spatial and Temporal Mixing Conditions

Cited by in corpus (1)

• Realizable monotonicity for continuous-time Markov processes