IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v150y2022icp446-509.html
   My bibliography  Save this article

Heavy range of the randomly biased walk on Galton–Watson trees in the slow movement regime

Author

Listed:
  • Chen, Xinxin

Abstract

We consider the randomly biased random walk on trees in the slow movement regime as in Hu and Shi (2016), whose potential is given by a branching random walk in the boundary case. We study the heavy range up to the nth return to the root, i.e., the number of edges visited more than kn times. For kn=nθ with θ∈(0,1), we obtain the convergence in probability of the rescaled heavy range, which improves one result of Andreoletti and Diel (2020).

Suggested Citation

  • Chen, Xinxin, 2022. "Heavy range of the randomly biased walk on Galton–Watson trees in the slow movement regime," Stochastic Processes and their Applications, Elsevier, vol. 150(C), pages 446-509.
    • Handle: RePEc:eee:spapps:v:150:y:2022:i:c:p:446-509
    DOI: 10.1016/j.spa.2022.04.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414922001077
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2022.04.018?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.

    References listed on IDEAS

    as
    1. Andreoletti, Pierre & Diel, Roland, 2020. "The heavy range of randomly biased walks on trees," Stochastic Processes and their Applications, Elsevier, vol. 130(2), pages 962-999.
    Full references (including those not matched with items on IDEAS)

    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.

      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:150:y:2022:i:c:p:446-509. 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: 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.