On the thermodynamic limit for a onedimensional sandpile process
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 nonlocality 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 October 1998
 DOI:
 10.48550/arXiv.math/9810093
 arXiv:
 arXiv:math/9810093
 Bibcode:
 1998math.....10093M
 Keywords:

 Probability