The Abelian sandpile model on an infinite tree

The Abelian sandpile model on an infinite tree

Christian Maes, Frank Redig, and Ellen Saada

Source: Ann. Probab. Volume 30, Number 4 (2002), 2081-2107.

Abstract

We consider the standard Abelian sandpile process on the Bethe lattice. We show the existence of the thermodynamic limit for the finite volume stationary measures and the existence of a unique infinite volume Markov process exhibiting features of self-organized criticality.

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Primary Subjects: 82C22

Secondary Subjects: 60K35

Keywords: Sandpile dynamics; nonlocal interactions; interacting particle systems; thermodynamic limit

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Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.aop/1039548382
Digital Object Identifier: doi:10.1214/aop/1039548382
Mathematical Reviews number (MathSciNet): MR1944016
Zentralblatt MATH identifier: 1013.60075

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CNRS, UMR 6085 UNIVERSITÉ DE ROUEN 76821 MONT-SAINT-AIGNAN CEDEX FRANCE E-MAIL: Ellen.Saada@univ-rouen.fr

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