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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
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    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)

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