IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v122y2012i3p1129-1153.html
   My bibliography  Save this article

k-independent percolation on trees

Author

Listed:
  • Mathieu, Pierre
  • Temmel, Christoph

Abstract

Consider the class of k-independent bond or site percolations with parameter p on a tree T. We derive tight bounds on p for both almost sure percolation and almost sure nonpercolation. The bounds are continuous functions of k and the branching number of T. This extends previous results by Lyons for the independent case (k=0) and by Balister & Bollobás for 1-independent bond percolations. Central to our argumentation are moment method bounds à la Lyons supplemented by explicit percolation models à la Balister & Bollobás. An indispensable tool is the minimality and explicit construction of Shearer’s measure on the k-fuzz of Z.

Suggested Citation

  • Mathieu, Pierre & Temmel, Christoph, 2012. "k-independent percolation on trees," Stochastic Processes and their Applications, Elsevier, vol. 122(3), pages 1129-1153.
    • Handle: RePEc:eee:spapps:v:122:y:2012:i:3:p:1129-1153
    DOI: 10.1016/j.spa.2011.10.014
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414911002754
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2011.10.014?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.

    Citations

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


    Cited by:

    1. Christoph Temmel, 2014. "Shearer’s Measure and Stochastic Domination of Product Measures," Journal of Theoretical Probability, Springer, vol. 27(1), pages 22-40, March.

    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:122:y:2012:i:3:p:1129-1153. 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.