@article{EJP640,
author = {Ronald Meester and Anne Fey-den Boer and Haiyan Liu},
title = {Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model},
journal = {Electron. J. Probab.},
fjournal = {Electronic Journal of Probability},
volume = {14},
year = {2009},
keywords = {Sandpile, stationary distribution, coupling, critical density, stabilizability},
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 $0\leq a < b\leq 1$. 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 $d\geq1$, 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 $\rho < \frac{1}{2}$, $\mu$ is stabilizable; for all $\rho\geq 1$, $\mu$ is not stabilizable; for $\frac{1}{2}\leq \rho<1$, when $\rho$ is near to $\frac{1}{2}$ or $1$, both possibilities can occur.},
pages = {no. 32, 895-911},
issn = {1083-6489},
doi = {10.1214/EJP.v14-640},
url = {http://ejp.ejpecp.org/article/view/640}}