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Abelian sandpiles: an overview and results on certain transitive graphs


Reference:

Jarai, A. A., 2012. Abelian sandpiles: an overview and results on certain transitive graphs. Markov Processes and Related Fields, 18 (1), pp. 111-156.

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    Abstract

    We review the Majumdar-Dhar bijection between recurrent states of the Abelian sandpile model and spanning trees. We generalize earlier results of Athreya and Jarai on the infinite volume limit of the stationary distribution of the sandpile model on Z^d, d >= 2, to a large class of graphs. This includes: (i) graphs on which the wired spanning forest is connected and has one end; (ii) transitive graphs with volume growth at least c n^5 on which all bounded harmonic functions are constant. We also extend a result of Maes, Redig and Saada on the stationary distribution of sandpiles on infinite regular trees, to arbitrary exhaustions.

    Details

    Item Type Articles
    CreatorsJarai, A. A.
    Related URLs
    URLURL Type
    http://arxiv.org/abs/1106.5358v2Free Full-text
    DepartmentsFaculty of Science > Mathematical Sciences
    RefereedYes
    StatusPublished
    ID Code26664

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