IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v142y2018icp17-22.html
   My bibliography  Save this article

A proof of the transfer-current theorem in absence of reversibility

Author

Listed:
  • Avena, L.
  • Gaudillière, A.

Abstract

The transfer-current theorem is a well-known result in probability theory stating that edges in a uniform spanning tree of an undirected graph form a determinantal process with kernel interpretable in terms of flows. Its original derivation due to Burton and Pemantle (1993) is based on a clever induction using comparison of random walks with electrical networks. Several variants of this celebrated result have recently appeared in the literature. In this paper we give an elementary proof of an extension of this theorem when the underlying graph is directed, irreducible and finite. Further, we give a characterization of the corresponding determinantal kernel in terms of flows extending the kernel given by Burton–Pemantle to the non-reversible setting.

Suggested Citation

  • Avena, L. & Gaudillière, A., 2018. "A proof of the transfer-current theorem in absence of reversibility," Statistics & Probability Letters, Elsevier, vol. 142(C), pages 17-22.
    • Handle: RePEc:eee:stapro:v:142:y:2018:i:c:p:17-22
    DOI: 10.1016/j.spl.2018.06.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S016771521830230X
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2018.06.007?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:stapro:v:142:y:2018:i:c:p:17-22. 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/622892/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.