A non-ergodic probabilistic cellular automaton with a unique invariant measure

We exhibit a Probabilistic Cellular Automaton (PCA) on { 0 , 1 } Z with 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.

MoreLess

Year of publication:	2011
Authors:	Chassaing, Philippe ; Mairesse, Jean
Published in:	Stochastic Processes and their Applications. - Elsevier, ISSN 0304-4149. - Vol. 121.2011, 11, p. 2474-2487
Publisher:	Elsevier
Keywords:	Probabilistic cellular automaton Interacting particle system Ergodicity

More details

Type of publication:	Article
Source:	RePEc - Research Papers in Economics

Persistent link: https://www.econbiz.de/10009318783