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Minimal Configurations and Sandpile Measures

Author

Listed:
  • Antal A. Járai

    (University of Bath)

  • Nicolás Werning

    (University of Reading)

Abstract

We give a new simple construction of the sandpile measure on an infinite graph G, under the sole assumption that each tree in the Wired Uniform Spanning Forest on G has one end almost surely. For the so-called generalized minimal configurations, the limiting probability on G exists even without this assumption. We also give determinantal formulas for minimal configurations on general graphs in terms of the transfer current matrix.

Suggested Citation

  • Antal A. Járai & Nicolás Werning, 2014. "Minimal Configurations and Sandpile Measures," Journal of Theoretical Probability, Springer, vol. 27(1), pages 153-167, March.
    • Handle: RePEc:spr:jotpro:v:27:y:2014:i:1:d:10.1007_s10959-012-0446-z
    DOI: 10.1007/s10959-012-0446-z
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    References listed on IDEAS

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    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. Dhar, Deepak, 2006. "Theoretical studies of self-organized criticality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 369(1), pages 29-70.
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    Cited by:

    1. 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.

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