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March 2009 Stabilizability and percolation in the infinite volume sandpile model
Anne Fey, Ronald Meester, Frank Redig
Ann. Probab. 37(2): 654-675 (March 2009). DOI: 10.1214/08-AOP415

Abstract

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.

Citation

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Anne Fey. Ronald Meester. Frank Redig. "Stabilizability and percolation in the infinite volume sandpile model." Ann. Probab. 37 (2) 654 - 675, March 2009. https://doi.org/10.1214/08-AOP415

Information

Published: March 2009
First available in Project Euclid: 30 April 2009

zbMATH: 1165.60033
MathSciNet: MR2510019
Digital Object Identifier: 10.1214/08-AOP415

Subjects:
Primary: 60G99, 60J25, 60K35

Rights: Copyright © 2009 Institute of Mathematical Statistics

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Vol.37 • No. 2 • March 2009
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