The Annals of Probability
- Ann. Probab.
- Volume 37, Number 2 (2009), 654-675.
Stabilizability and percolation in the infinite volume sandpile model
We study the sandpile model in infinite volume on ℤd. In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure μ, are μ-almost surely stabilizable. We prove that stabilizability does not depend on the particular procedure of stabilization we adopt. In d=1 and μ a product measure with density ρ=1 (the known critical value for stabilizability in d=1) with a positive density of empty sites, we prove that μ is not stabilizable.
Furthermore, we study, for values of ρ such that μ is stabilizable, percolation of toppled sites. We find that for ρ>0 small enough, there is a subcritical regime where the distribution of a cluster of toppled sites has an exponential tail, as is the case in the subcritical regime for ordinary percolation.
Ann. Probab., Volume 37, Number 2 (2009), 654-675.
First available in Project Euclid: 30 April 2009
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J25: Continuous-time Markov processes on general state spaces 60G99: None of the above, but in this section
Fey, Anne; Meester, Ronald; Redig, Frank. Stabilizability and percolation in the infinite volume sandpile model. Ann. Probab. 37 (2009), no. 2, 654--675. doi:10.1214/08-AOP415. https://projecteuclid.org/euclid.aop/1241099924