IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v125y2015i11p4102-4116.html
   My bibliography  Save this article

Factorization formulas for 2D critical percolation, revisited

Author

Listed:
  • Conijn, R.P.

Abstract

We consider critical site percolation on the triangular lattice in the upper half-plane. Let u1,u2 be two sites on the boundary and w a site in the interior. It was predicted by Simmons et al. (2007) that the ratio P(nu1↔nu2↔nw)2/P(nu1↔nu2)⋅P(nu1↔nw)⋅P(nu2↔nw) converges to KF as n→∞, where x↔y denotes that x and y are in the same cluster, and KF is a constant. Beliaev and Izyurov (2012) proved an analog of this in the scaling limit. We prove, using their result and a generalized coupling argument, the earlier mentioned prediction. Furthermore we prove a factorization formula for P(nu2↔[nu1,nu1+s];nw↔[nu1,nu1+s]), where s>0.

Suggested Citation

  • Conijn, R.P., 2015. "Factorization formulas for 2D critical percolation, revisited," Stochastic Processes and their Applications, Elsevier, vol. 125(11), pages 4102-4116.
    • Handle: RePEc:eee:spapps:v:125:y:2015:i:11:p:4102-4116
    DOI: 10.1016/j.spa.2015.05.017
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414915001398
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2015.05.017?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.

    More about this item

    Keywords

    Critical percolation; Scaling limit;

    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:eee:spapps:v:125:y:2015:i:11:p:4102-4116. 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.