Dualities for Multi-State Probabilistic Cellular Automata
Probability
2017-02-15 v5
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.
Cite
@article{arxiv.math/0607206,
title = {Dualities for Multi-State Probabilistic Cellular Automata},
author = {F. J. Lopez and G. Sanz and M. Sobottka},
journal= {arXiv preprint arXiv:math/0607206},
year = {2017}
}
Comments
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