IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v123y2013i9p3588-3621.html
   My bibliography  Save this article

Subdiffusivity of random walk on the 2D invasion percolation cluster

Author

Listed:
  • Damron, Michael
  • Hanson, Jack
  • Sosoe, Philippe

Abstract

We derive quenched subdiffusive lower bounds for the exit time τ(n) from a box of size n for the simple random walk on the planar invasion percolation cluster. The first part of the paper is devoted to proving an almost sure analogue of H. Kesten’s subdiffusivity theorem for the random walk on the incipient infinite cluster and the invasion percolation cluster using ideas of M. Aizenman, A. Burchard and A. Pisztora. The proof combines lower bounds on the intrinsic distance in these graphs and general inequalities for reversible Markov chains. In the second part of the paper, we present a sharpening of Kesten’s original argument, leading to an explicit almost sure lower bound for τ(n) in terms of percolation arm exponents. The methods give τ(n)≥n2+ϵ0+κ, where ϵ0>0 depends on the intrinsic distance and κ can be taken to be 5384 on the hexagonal lattice.

Suggested Citation

  • Damron, Michael & Hanson, Jack & Sosoe, Philippe, 2013. "Subdiffusivity of random walk on the 2D invasion percolation cluster," Stochastic Processes and their Applications, Elsevier, vol. 123(9), pages 3588-3621.
  • Handle: RePEc:eee:spapps:v:123:y:2013:i:9:p:3588-3621
    DOI: 10.1016/j.spa.2013.04.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414913001142
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.spa.2013.04.018?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.

    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:123:y:2013:i:9:p:3588-3621. 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.