Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

Details Infinite volume limit of the Abelian sandpile model in dimensions d >= 3 Infinite volume limit of the Abelian sandpile model in dimensions d >= 3

2004-08-04

arxiv.org/abs/math/0408060v3

Probab. Theory Related Fields 141 (2008), no. 1-2, 181-212

Mathematics

Probability

First version: LaTeX; 29 pages. Revised version: LaTeX; 29 pages. The main result of the paper has been extended to all dimens

Scientific paper

10.1007/s00440-007-0083-0

We study the Abelian sandpile model on Z^d. In dimensions at least 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit mu of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure mu, and study ergodic properties of this process. The main techniques we use are a connection between the statistics of waves and uniform two-component spanning trees and results on the uniform spanning tree measure on Z^d.

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