Abelian Sandpiles and the Harmonic Model

Speaker  Klaus Schmidt

Host  Yuval Peres

Affiliation  University of Vienna

Duration  00:51:52

Date recorded  17 August 2011

There exists an entropy-preserving equivariant surjective map from the d-dimensional critical sandpile model to a certain closed, shift-invariant subgroup of the Cartesian product of infinitely many cycles, one for each node of the d-dimensional integer lattice (the 'harmonic model'). A similar map can be constructed for the dissipative abelian sandpile model and be used to prove uniqueness and the Bernoulli property of the measure of maximal entropy for that model. (Joint work with Evgeny Verbitskiy)

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