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Abelian Sandpiles and the Harmonic Model

Schmidt, K. & Verbitskiy, E., Dec-2009, In : Communications in Mathematical Physics. 292, 3, p. 721-759 39 p.

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DOI

We present a construction of an entropy-preserving equivariant surjective map from the d-dimensional critical sandpile model to a certain closed, shift-invariant subgroup of T(Zd) (the 'harmonicmodel'). A similar map is constructed for the dissipative abelian sandpile model and is used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model.

Original languageEnglish
Pages (from-to)721-759
Number of pages39
JournalCommunications in Mathematical Physics
Volume292
Issue number3
Publication statusPublished - Dec-2009

    Keywords

  • SELF-ORGANIZED CRITICALITY, INFINITE VOLUME LIMIT, ENTROPY, AUTOMORPHISMS

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