IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v130y2020i6p3477-3498.html
   My bibliography  Save this article

On the speed and spectrum of mean-field random walks among random conductances

Author

Listed:
  • Collevecchio, Andrea
  • Jung, Paul

Abstract

We study random walk among random conductance (RWRC) on complete graphs with n vertices. The conductances are i.i.d. and the sum of conductances emanating from a single vertex asymptotically has an infinitely divisible distribution corresponding to a Lévy subordinator with infinite mass at 0. We show that, under suitable conditions, the empirical spectral distribution of the random transition matrix associated to the RWRC converges weakly, as n→∞, to a symmetric deterministic measure on [−1,1], in probability with respect to the randomness of the conductances. In short time scales, the limiting underlying graph of the RWRC is a Poisson Weighted Infinite Tree, and we analyze the RWRC on this limiting tree. In particular, we show that the transient RWRC exhibits a phase transition in which it has positive or weakly zero speed when the mean of the largest conductance is finite or infinite, respectively.

Suggested Citation

  • Collevecchio, Andrea & Jung, Paul, 2020. "On the speed and spectrum of mean-field random walks among random conductances," Stochastic Processes and their Applications, Elsevier, vol. 130(6), pages 3477-3498.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:6:p:3477-3498
    DOI: 10.1016/j.spa.2019.10.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414918304848
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2019.10.001?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. Gantert, Nina & Müller, Sebastian & Popov, Serguei & Vachkovskaia, Marina, 2012. "Random walks on Galton–Watson trees with random conductances," Stochastic Processes and their Applications, Elsevier, vol. 122(4), pages 1652-1671.
    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.
    1. Bowditch, Adam, 2019. "Central limit theorems for biased randomly trapped random walks on Z," Stochastic Processes and their Applications, Elsevier, vol. 129(3), pages 740-770.

    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:130:y:2020:i:6:p:3477-3498. 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.