Stabilizability and percolation in the infinite volume sandpile model
نویسندگان
چکیده
منابع مشابه
Stabilizability and Percolation in the Infinite Volume Sandpile Model
We study the sandpile model in infinite volume on Z. 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 f...
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Since its introduction by Bak,Tang and Wiesenfeld, the abelian sandpile dynamics has been studied extensively in finite volume. There are many problems posed by the existence of a sandpile dynamics in an infinite volume S: its invariant distribution should be the thermodynamic limit (does the latter exist?) of the invariant measure for the finite volume dynamics; the extension of the sand grain...
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We define stabilizability of an infinite volume height configuration and of a probability measure on height configurations. We show that for high enough densities, a probability measure cannot be stabilized. We also show that in some sense the thermodynamic limit of the uniform measures on the recurrent configurations of the abelian sandpile model (ASM) is a maximal element of the set of stabil...
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We study the Abelian sandpile model on Z. 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 st...
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We show that Zhang’s sandpile model (N , [a, b]) on N sites and with uniform additions on [a, b] has a unique stationary measure for all 0 ≤ a < b ≤ 1. This generalizes earlier results of [6] where this was shown in some special cases. We define the infinite volume Zhang’s sandpile model in dimension d ≥ 1, in which topplings occur according to a Markov toppling process, and we study the stabil...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 2009
ISSN: 0091-1798
DOI: 10.1214/08-aop415