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

Antal A Jarai, Frank Redig

Research output: Contribution to journalArticlepeer-review

15 Citations (Scopus)

Abstract

We study the Abelian sandpile model on ℤd . In d ≥ 3 we prove existence of the infinite volume addition operator, almost surely with respect to the infinite volume limit μ of the uniform measures on recurrent configurations. We prove the existence of a Markov process with stationary measure μ, 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 forest measure on ℤd .
Original languageEnglish
Pages (from-to)181-212
Number of pages32
JournalProbability Theory and Related Fields
Volume141
Issue number1-2
DOIs
Publication statusPublished - 2008

Fingerprint Dive into the research topics of 'Infinite volume limit of the Abelian sandpile model in dimensions d ≥ 3'. Together they form a unique fingerprint.

Cite this