Abelian Sandpiles and the Harmonic Model

  • Klaus SchmidtEmail author
  • Evgeny Verbitskiy
Open Access


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 \({\mathbb{T}^{\mathbb{Z}^d}}\) (the ‘harmonic model’). 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.


Entropy Span Tree Maximal Entropy Topological Entropy Compact Abelian Group 
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E.V. would like to acknowledge the hospitality of the Erwin Schrödinger Institute (Vienna), where part of this work was done. E.V. is also grateful to Frank Redig, Marius van der Put and Thomas Tsang for illuminating discussions. K.S. would like to thank EURANDOM (Eindhoven) and MSRI (Berkeley), for hospitality and support during part of this work.

Open Access

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© The Author(s) 2009

Authors and Affiliations

  1. 1.Mathematics InstituteUniversity of ViennaViennaAustria
  2. 2.Erwin Schrödinger Institute for Mathematical PhysicsViennaAustria
  3. 3.Philips ResearchEindhovenThe Netherlands
  4. 4.Department of MathematicsUniversity of GroningenGroningenThe Netherlands

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