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Abelian Sandpiles and the Harmonic Model

2009/01/20 by Klaus Schmidt, Evgeny Verbitskiy · 1 citation
Mathematics · Physics and Astronomy · #math.DS #math-ph #math.MP #msc:37B10 #msc:37A05 #msc:37A45 #msc:37D30 #msc:82C22

paper · pdf · doi:10.1007/s00220-009-0884-3

arxiv created 2009/01/20 · arxiv updated 2015/05/12

Abstract

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 \mathbbTd (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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