IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v13y2000i3d10.1023_a1007806427774.html
   My bibliography  Save this article

Dual Families of Interacting Particle Systems on Graphs

Author

Listed:
  • Aidan Sudbury

    (Monash University)

Abstract

A simple condition for IPS (Interacting Particle Systems) with nearest neighbor interactions to be self-dual is given. It follows that any IPS with the contact transition and no spontaneous birth is self-dual. It is shown that families of IPS exist in which every IPS is dual to every other, and such that for every pair of IPS, one is a “thinning” of the other. Further, all such IPS have the same form for an equilibrium distribution when expressed in terms of survival probabilities. Convergence results from a wide class of initial infinite measures follow.

Suggested Citation

  • Aidan Sudbury, 2000. "Dual Families of Interacting Particle Systems on Graphs," Journal of Theoretical Probability, Springer, vol. 13(3), pages 695-716, July.
    • Handle: RePEc:spr:jotpro:v:13:y:2000:i:3:d:10.1023_a:1007806427774
    DOI: 10.1023/A:1007806427774
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1023/A:1007806427774
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1023/A:1007806427774?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. Belitsky, Vladimir & Ferrari, Pablo A. & Konno, Norio & Liggett, Thomas M., 1997. "A strong correlation inequality for contact processes and oriented percolation," Stochastic Processes and their Applications, Elsevier, vol. 67(2), pages 213-225, May.
    2. Sudbury, Aidan, 1997. "The convergence of the biased annihilating branching process and the double-flipping process in d," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 255-264, June.
    3. Bramson, Maury & Wan-ding, Ding & Durrett, Rick, 1991. "Annihilating branching processes," Stochastic Processes and their Applications, Elsevier, vol. 37(1), pages 1-17, February.
    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. Makoto Katori & Norio Konno & Aidan Sudbury & Hideki Tanemura, 2004. "Dualities for the Domany–Kinzel Model," Journal of Theoretical Probability, Springer, vol. 17(1), pages 131-144, January.
    2. Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.
    3. Anja Sturm & Jan M. Swart, 2018. "Pathwise Duals of Monotone and Additive Markov Processes," Journal of Theoretical Probability, Springer, vol. 31(2), pages 932-983, June.

    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. Sudbury, Aidan, 1997. "The convergence of the biased annihilating branching process and the double-flipping process in d," Stochastic Processes and their Applications, Elsevier, vol. 68(2), pages 255-264, June.
    2. Alili, Smail & Ignatiouk-Robert, Irina, 2001. "On the surviving probability of an annihilating branching process and application to a nonlinear voter model," Stochastic Processes and their Applications, Elsevier, vol. 93(2), pages 301-316, June.
    3. Jan Niklas Latz & Jan M. Swart, 2023. "Commutative Monoid Duality," Journal of Theoretical Probability, Springer, vol. 36(2), pages 1088-1115, June.

    More about this item

    Keywords

    Interacting Particle Systems; duality;

    Statistics

    Access and download statistics

    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:spr:jotpro:v:13:y:2000:i:3:d:10.1023_a:1007806427774. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.