CHARACTERISTIC EXPONENTS FOR 2-DIMENSIONAL BOOTSTRAP PERCOLATION
成果类型：
Article
署名作者：
ANDJEL, ED
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989275
发表日期：
1993
页码：
926-935
关键词：
摘要：
Bootstrap percolation is a model in which an element of Z2 becomes occupied in one time unit if two appropriately chosen neighbors are occupied. Schonmann [4] proved that starting from a Bernoulli product measure of positive density, the distribution of the time needed to occupy the origin decays exponentially. We show that for alpha > 1, the exponent can be taken as deltap2alpha for some delta > 0, thus showing that the associated characteristic exponent is at most two. Another characteristic exponent associated to this model is shown to be equal to one.