STABILIZABILITY AND PERCOLATION IN THE INFINITE VOLUME SANDPILE MODEL
成果类型：
Article
署名作者：
Fey, Anne; Meester, Ronald; Redig, Frank
署名单位：
Vrije Universiteit Amsterdam; Leiden University; Leiden University - Excl LUMC
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/08-AOP415
发表日期：
2009
页码：
654-675
关键词：
摘要：
We study the sandpile model in infinite volume on Z(d). In particular, we are interested in the question whether or not initial configurations, chosen according to a stationary measure mu, are mu-almost surely stabilizable. We prove that stabilizability does not depend on the particular procedure of stabilization we adopt. In d = 1 and mu a product measure with density rho = 1 (the known critical value for stabilizability in d = 1) with a positive density of empty sites, we prove that mu is not stabilizable. Furthermore, we study, for values of rho such that mu is stabilizable, percolation of toppled sites. We find that for rho > 0 small enough, there is a subcritical regime where the distribution of a cluster of toppled sites has an exponential tail, as is the case in the subcritical regime for ordinary percolation.