IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v121y2011i11p2474-2487.html
   My bibliography  Save this article

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

Author

Listed:
  • Chassaing, Philippe
  • Mairesse, Jean

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.

Suggested Citation

  • Chassaing, Philippe & Mairesse, Jean, 2011. "A non-ergodic probabilistic cellular automaton with a unique invariant measure," Stochastic Processes and their Applications, Elsevier, vol. 121(11), pages 2474-2487, November.
    • Handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2474-2487
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911001566
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Casse, Jérôme & Marckert, Jean-François, 2015. "Markovianity of the invariant distribution of probabilistic cellular automata on the line," Stochastic Processes and their Applications, Elsevier, vol. 125(9), pages 3458-3483.
    2. Jahnel, Benedikt & Külske, Christof, 2015. "A class of non-ergodic probabilistic cellular automata with unique invariant measure and quasi-periodic orbit," Stochastic Processes and their Applications, Elsevier, vol. 125(6), pages 2427-2450.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:spapps:v:121:y:2011:i:11:p:2474-2487. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/505572/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.