C. Maes, F. Redig, E. Saada, A. Van Moffaert
On the thermodynamic limit for a one-dimensional sandpile process
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ABSTRACT.  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.