IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v462y2016icp793-806.html
   My bibliography  Save this article

Critical value for the contact process with random recovery rates and edge weights on regular tree

Author

Listed:
  • Xue, Xiaofeng

Abstract

In this paper we are concerned with contact processes with random recovery rates and edge weights on rooted regular trees TN. Let ρ and ξ be two nonnegative random variables such that P(ϵ≤ξ<+∞,ρ≤M)=1 for some ϵ,M>0. For each vertex x on TN, ξ(x) is an independent copy of ξ while for each edge e on TN, ρ(e) is an independent copy of ρ. An infected vertex x becomes healthy at rate ξ(x) while an infected vertex y infects an healthy neighbor z at rate proportional to ρ(y,z). For this model, we prove that the critical value under the annealed measure approximately equals (NEρE1ξ)−1 as N grows to infinity. Furthermore, we show that the critical value under the quenched measure equals that under the annealed measure when the cluster containing the root formed with edges with positive weights is infinite.

Suggested Citation

  • Xue, Xiaofeng, 2016. "Critical value for the contact process with random recovery rates and edge weights on regular tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 793-806.
  • Handle: RePEc:eee:phsmap:v:462:y:2016:i:c:p:793-806
    DOI: 10.1016/j.physa.2016.06.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437116302692
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000

    File URL: https://libkey.io/10.1016/j.physa.2016.06.001?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. Peterson, Jonathon, 2011. "The contact process on the complete graph with random vertex-dependent infection rates," Stochastic Processes and their Applications, Elsevier, vol. 121(3), pages 609-629, March.
    2. Xue, Xiaofeng, 2016. "Critical value for contact processes on clusters of oriented bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 205-215.
    3. Xue, Xiaofeng, 2013. "Contact processes with random connection weights on regular graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4749-4759.
    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. Xue, Xiaofeng, 2016. "Critical value for contact processes on clusters of oriented bond percolation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 205-215.
    2. Xue, Xiaofeng, 2017. "Law of large numbers for the SIR model with random vertex weights on Erdős–Rényi graph," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 434-445.
    3. Xue, Xiaofeng, 2013. "Contact processes with random connection weights on regular graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(20), pages 4749-4759.
    4. Xiaofeng Xue, 2018. "Asymptotic of the Critical Value of the Large-Dimensional SIR Epidemic on Clusters," Journal of Theoretical Probability, Springer, vol. 31(4), pages 2343-2365, December.

    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:phsmap:v:462:y:2016:i:c:p:793-806. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.