Abelian Sandpiles and the Harmonic Model

Details Abelian Sandpiles and the Harmonic Model Abelian Sandpiles and the Harmonic Model

2009-01-20

arxiv.org/abs/0901.3124v1

Mathematics

Dynamical Systems

Scientific paper

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.

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