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

Philippe Chassaing and Jean Mairesse

Stochastic Processes and their Applications, 2011, vol. 121, issue 11, 2474-2487

Abstract: 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.

Keywords: Probabilistic; cellular; automaton; Interacting; particle; system; Ergodicity (search for similar items in EconPapers)
Date: 2011
References: View complete reference list from CitEc
Citations: View citations in EconPapers (2)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0304414911001566
Full text for ScienceDirect subscribers only

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:121:y:2011:i:11:p:2474-2487

Ordering information: This journal article can be ordered from
http://http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().