On the thermodynamic limit for a one-dimensional sandpile process

Details On the thermodynamic limit for a one-dimensional sandpile process On the thermodynamic limit for a one-dimensional sandpile process

1998-10-15

arxiv.org/abs/math/9810093v1

Mathematics

Probability

Scientific paper

Considering the standard abelian sandpile model in one dimension, we construct an infinite volume Markov process corresponding to its thermodynamic (infinite volume) limit. The main difficulty we overcome is the strong non-locality of the dynamics. However, using similar ideas as in recent extensions of the standard Gibbs formalism for lattice spin systems, we can identify a set of `good' configurations on which the dynamics is effectively local. We prove that every configuration converges in a finite time to the unique invariant measure.

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