The Abelian Sandpile Model on an Infinite Tree
Christian Maes, Frank Redig, Ellen Saada
TL;DR
This paper studies the Abelian sandpile model on an infinite tree (Bethe lattice), proving the existence of a stable infinite-volume process that demonstrates self-organized criticality, advancing understanding of critical phenomena in such systems.
Contribution
It establishes the existence of a unique infinite-volume Markov process for the Abelian sandpile on an infinite tree, demonstrating self-organized criticality in this setting.
Findings
Existence of thermodynamic limit for finite volume measures
Existence of a unique infinite-volume Markov process
Features of self-organized criticality confirmed
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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Taxonomy
TopicsTheoretical and Computational Physics · Stochastic processes and statistical mechanics · Mathematical Dynamics and Fractals