IDEAS home Printed from https://ideas.repec.org/a/spr/metcap/v23y2021i1d10.1007_s11009-020-09773-2.html
   My bibliography  Save this article

Structure of the Particle Population for a Branching Random Walk with a Critical Reproduction Law

Author

Listed:
  • Daria Balashova

    (Lomonosov Moscow State University)

  • Stanislav Molchanov

    (University of North Carolina at Charlotte
    National Research University Higher School of Economics)

  • Elena Yarovaya

    (Lomonosov Moscow State University)

Abstract

We consider a continuous-time symmetric branching random walk on the d-dimensional lattice, d ≥ 1, and assume that at the initial moment there is one particle at every lattice point. Moreover, we assume that the underlying random walk has a finite variance of jumps and the reproduction law is described by a continuous-time Markov branching process (a continuous-time analog of a Bienamye-Galton-Watson process) at every lattice point. We study the structure of the particle subpopulation generated by the initial particle situated at a lattice point x. We replay why vanishing of the majority of subpopulations does not affect the convergence to the steady state and leads to clusterization for lattice dimensions d = 1 and d = 2.

Suggested Citation

  • Daria Balashova & Stanislav Molchanov & Elena Yarovaya, 2021. "Structure of the Particle Population for a Branching Random Walk with a Critical Reproduction Law," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 85-102, March.
    • Handle: RePEc:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09773-2
    DOI: 10.1007/s11009-020-09773-2
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s11009-020-09773-2
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s11009-020-09773-2?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. Stanislav Molchanov & Joseph Whitmeyer, 2017. "Stationary distributions in Kolmogorov-Petrovski- Piskunov-type models with an infinite number of particles," Mathematical Population Studies, Taylor & Francis Journals, vol. 24(3), pages 147-160, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Iuliia Makarova & Daria Balashova & Stanislav Molchanov & Elena Yarovaya, 2022. "Branching Random Walks with Two Types of Particles on Multidimensional Lattices," Mathematics, MDPI, vol. 10(6), pages 1-45, March.

    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. Yaqin Feng & Stanislav Molchanov & Elena Yarovaya, 2021. "Stability and Instability of Steady States for a Branching Random Walk," Methodology and Computing in Applied Probability, Springer, vol. 23(1), pages 207-218, March.

    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:spr:metcap:v:23:y:2021:i:1:d:10.1007_s11009-020-09773-2. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.