Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model
Ronald Meester, VU University Amsterdam
Anne Fey-den Boer, TU Delft
Haiyan Liu, VU University Amsterdam
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
Full text: PDF | PostScript
Copyright for articles published in this journal is retained by the authors, with first publication rights granted to the journal. By virtue of their appearance in this open access journal, articles are free to use, with proper attribution, in educational and other non-commercial settings.
The authors of papers published in EJP/ECP retain the copyright. We ask for the permission to use the material in any form. We also require that the initial publication in EJP or ECP is acknowledged in any future publication of the same article.
Before a paper is published in the Electronic Journal of Probability or Electronic Communications in Probability we must receive a hard-copy of the copyright form. Please mail it to
Philippe Carmona
Laboratoire Jean Leray UMR 6629
Universite de Nantes,
2, Rue de la Houssinière BP 92208
F-44322 Nantes Cédex 03
France
You can also send it by FAX: (33|0) 2 51 12 59 12 to the attention of Philippe Carmona. You can even send a scanned jpeg or pdf of this copyright form to the managing editor ejpecpme@math.univ-nantes.fr. as an attached file.
If a paper has several authors, the corresponding author signs the copyright form on behalf of all the authors.