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Uniqueness of the stationary distribution and stabilizability in Zhang’s sandpile model

By Anne Fey-den Boer, Haiyan Liu and Ronald Meester

Abstract

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 stabilizability of initial configurations chosen according to some measure µ. We show that for a stationary ergodic measure µ with density ρ, for all ρ < 1, µ is stabilizable; for all ρ ≥ 1, µ is not stabilizable; for 1 2 possibilities can occur

Year: 2008
OAI identifier: oai:CiteSeerX.psu:10.1.1.311.2094
Provided by: CiteSeerX
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