| Título: | Uniqueness of the stationary distribution and stabilizability in Zhang's sandpile model |
| Autores: |
Meester, Ronald; VU University Amsterdam Fey-den Boer, Anne; TU Delft Liu, Haiyan; VU University Amsterdam |
| Fecha: | 2009-01-01 |
| Publicador: | Electronic journal of probability |
| Fuente: |
 |
| Tipo: |
Peer-reviewed Article |
| Tema: |
Sandpile, stationary distribution, coupling, critical density, stabilizability 60J27, 60F05, 60B10, 82B20 |
| Descripción: | 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. |
| Idioma: | No aplica |
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