98-648 C. Maes, F. Redig, E. Saada, A. Van Moffaert

On the thermodynamic limit for a one-dimensional sandpile process (54K, LaTeX 2e) Oct 15, 98

Abstract , Paper (src), View paper (auto. generated ps), Index of related papers

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.

Files: 98-648.src( 98-648.comments , 98-648.keywords , onedim2.tex )