The Annals of Probability

The Abelian sandpile model on an infinite tree

Christian Maes, Frank Redig, and Ellen Saada

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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.

Article information

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

Dates
First available in Project Euclid: 10 December 2002

Permanent link to this document
https://projecteuclid.org/euclid.aop/1039548382

Digital Object Identifier
doi:10.1214/aop/1039548382

Mathematical Reviews number (MathSciNet)
MR1944016

Zentralblatt MATH identifier
1013.60075

Subjects
Primary: 82C22: Interacting particle systems [See also 60K35]
Secondary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
Sandpile dynamics nonlocal interactions interacting particle systems thermodynamic limit

Citation

Maes, Christian; Redig, Frank; Saada, Ellen. The Abelian sandpile model on an infinite tree. Ann. Probab. 30 (2002), no. 4, 2081--2107. doi:10.1214/aop/1039548382. https://projecteuclid.org/euclid.aop/1039548382


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References

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