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 -