IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i6p2427-2450.html
   My bibliography  Save this article

A class of non-ergodic probabilistic cellular automata with unique invariant measure and quasi-periodic orbit

Author

Listed:
  • Jahnel, Benedikt
  • Külske, Christof

Abstract

We provide an example of a discrete-time Markov process on the three-dimensional infinite integer lattice with Zq-invariant Bernoulli-increments which has as local state space the cyclic group Zq. We show that the system has a unique invariant measure, but remarkably possesses an invariant set of measures on which the dynamics is conjugate to an irrational rotation on the continuous sphere S1. The update mechanism we construct is exponentially well localized on the lattice.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:6:p:2427-2450
    DOI: 10.1016/j.spa.2015.01.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915000174
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.01.006?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

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

    References listed on IDEAS

    as
    1. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

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


    Cited by:

    1. Cirillo, Emilio N.M. & Nardi, Francesca R. & Spitoni, Cristian, 2021. "Phase transitions in random mixtures of elementary cellular automata," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 573(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    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.

    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:125:y:2015:i:6:p:2427-2450. 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.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with 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.