Dualities for Multi-State Probabilistic Cellular Automata
arXiv:math/0607206 · doi:10.1088/1742-5468/2008/05/P05006
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 existence of a dual are provided. The results are applied to wide classes of PCA which include multi-opinion voter models, competition models and the Domany-Kinzel model.
22 pages A new version in which the text and the proofs were revised in order to become correct and more accessible for the reader