Dualities for multi-state probabilistic cellular automata

Abstract

In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced.Using this duality, an ergodicity result for processes having a dual is proved. Also,conditions on the probabilities defining the evolution of the processes for the existenceof a dual are provided. The results are applied to wide classes of PCA whichinclude multi-opinion voter models, competition models and the Domany–Kinzelmodel.