Dualities for Multi-State Probabilistic Cellular Automata

Details Dualities for Multi-State Probabilistic Cellular Automata Dualities for Multi-State Probabilistic Cellular Automata

2006-07-07

arxiv.org/abs/math/0607206v4

Journal of Statistical Mechanics (2008) P05006

Mathematics

Probability

22 pages A new version in which the text and the proofs were revised in order to become correct and more accessible for the re

Scientific paper

10.1088/1742-5468/2008/05/P05006

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.

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