Abelian Sandpiles and the Harmonic Model

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 ${\mathbb{T}}^{{\mathbb{Z}}^d}$ (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.

References in corpus (3)

• The abelian sandpile and related models
• Infinite volume limit of the Abelian sandpile model in dimensions d >= 3
• Uniqueness of maximal entropy measure on essential spanning forests

Cited by in corpus (6)

• Sandpiles on the square lattice
• Cut-off for sandpiles on tiling graphs
• Anchored burning bijections on finite and infinite graphs
• Galois orbits of torsion points near atoral sets
• Homoclinically expansive actions and a Garden of Eden theorem for harmonic models
• Topology of a Uniform Spanning Tree on a Cylinder