A non-ergodic probabilistic cellular automaton with a unique invariant measure
Formal Languages and Automata Theory
2011-07-11 v3 Discrete Mathematics
Probability
Abstract
We exhibit a Probabilistic Cellular Automaton (PCA) on the integers with an alphabet and a neighborhood of size 2 which is non-ergodic although it has a unique invariant measure. This answers by the negative an old open question on whether uniqueness of the invariant measure implies ergodicity for a PCA.
Cite
@article{arxiv.1009.0143,
title = {A non-ergodic probabilistic cellular automaton with a unique invariant measure},
author = {Philippe Chassaing and Jean Mairesse},
journal= {arXiv preprint arXiv:1009.0143},
year = {2011}
}
Comments
To appear in Stochastic Processes and their Applications