IDEAS home Printed from https://ideas.repec.org/a/spr/jotpro/v34y2021i1d10.1007_s10959-019-00962-5.html
   My bibliography  Save this article

Asymptotic Height Distribution in High-Dimensional Sandpiles

Author

Listed:
  • Antal A. Járai

    (University of Bath)

  • Minwei Sun

    (University of Bath)

Abstract

We give an asymptotic formula for the single-site height distribution of Abelian sandpiles on $$\mathbb {Z}^d$$ Z d as $$d \rightarrow \infty $$ d → ∞ , in terms of $$\mathsf {Poisson}(1)$$ Poisson ( 1 ) probabilities. We provide error estimates.

Suggested Citation

  • Antal A. Járai & Minwei Sun, 2021. "Asymptotic Height Distribution in High-Dimensional Sandpiles," Journal of Theoretical Probability, Springer, vol. 34(1), pages 349-362, March.
    • Handle: RePEc:spr:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00962-5
    DOI: 10.1007/s10959-019-00962-5
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10959-019-00962-5
    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/s10959-019-00962-5?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. Majumdar, S.N. & Dhar, Deepak, 1992. "Equivalence between the Abelian sandpile model and the q→0 limit of the Potts model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 185(1), pages 129-145.
    2. Antal A. Járai & Nicolás Werning, 2014. "Minimal Configurations and Sandpile Measures," Journal of Theoretical Probability, Springer, vol. 27(1), pages 153-167, March.
    3. Dhar, Deepak, 2006. "Theoretical studies of self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 29-70.
    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. Wu, Xiaoxia & Zhang, Lianzhu & Chen, Haiyan, 2017. "Spanning trees and recurrent configurations of a graph," Applied Mathematics and Computation, Elsevier, vol. 314(C), pages 25-30.
    2. Antal A. Járai & Nicolás Werning, 2014. "Minimal Configurations and Sandpile Measures," Journal of Theoretical Probability, Springer, vol. 27(1), pages 153-167, March.
    3. Kévin Perrot & Éric Rémila, 2015. "Emergence on Decreasing Sandpile Models," Post-Print halshs-01212069, HAL.
    4. Shapoval, A.B. & Shnirman, M.G., 2012. "The BTW mechanism on a self-similar image of a square: A path to unexpected exponents," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 15-20.
    5. Ding, Jin & Lu, Yong-Zai & Chu, Jian, 2013. "Studies on controllability of directed networks with extremal optimization," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(24), pages 6603-6615.
    6. Liao, Yunhua & Fang, Aixiang & Hou, Yaoping, 2013. "The Tutte polynomial of an infinite family of outerplanar, small-world and self-similar graphs," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4584-4593.
    7. Sokolov, Andrey & Melatos, Andrew & Kieu, Tien & Webster, Rachel, 2015. "Memory on multiple time-scales in an Abelian sandpile," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 295-301.
    8. Bosiljka Tadić & Roderick Melnik, 2020. "Modeling latent infection transmissions through biosocial stochastic dynamics," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-16, October.

    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:jotpro:v:34:y:2021:i:1:d:10.1007_s10959-019-00962-5. 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.