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Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model
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Ronald Meester, VU University Amsterdam
Anne Fey-den Boer, TU Delft
Haiyan Liu, VU University Amsterdam
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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 $0leq a < bleq 1$. This generalizes
earlier results of cite{anne} where this was shown in some special cases.
We define the infinite volume Zhang's sandpile model in dimension
$dgeq1$, in which topplings occur according to a Markov toppling
process, and we study the stabilizability of initial configurations
chosen according to some measure $mu$. We show that for a
stationary ergodic measure $mu$ with density $rho$, for all
$rho
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Full text: PDF
Pages: 895-911
Published on: April 27, 2009
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