TY - JOUR

T1 - Infinite volume limit of the Abelian sandpile model in dimensions d ≥ 3

AU - Jarai, Antal A

AU - Redig, Frank

PY - 2008

Y1 - 2008

N2 - 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 .

AB - 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 .

UR - http://www.scopus.com/inward/record.url?scp=38849153625&partnerID=8YFLogxK

UR - http://arxiv.org/abs/math/0408060v3

UR - http://dx.doi.org/10.1007/s00440-007-0083-0

U2 - 10.1007/s00440-007-0083-0

DO - 10.1007/s00440-007-0083-0

M3 - Article

SN - 0178-8051

VL - 141

SP - 181

EP - 212

JO - Probability Theory and Related Fields

JF - Probability Theory and Related Fields

IS - 1-2

ER -