SUBDIFFUSIVE FLUCTUATIONS FOR INTERNAL DIFFUSION-LIMITED AGGREGATION
成果类型：
Article
署名作者：
LAWLER, GF
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176988377
发表日期：
1995
页码：
71-86
关键词：
摘要：
Internal diffusion limited aggregation (internal DLA) is a cluster model in Z(d) where new points are added by starting random walkers at the origin and letting them run until they have found a new point to add to the cluster. It has been shown that the limiting shape of internal DLA. clusters is spherical. Here we show that for d greater than or equal to 2 the fluctuations are subdiffusive; in fact, that they are of order at most n(1/3), at least up to logarithmic corrections. More precisely, we show that for all sufficiently large n the cluster after m = [omega(d)n(d)] steps covers all points in the ball of radius n - n(1/3)(ln n)(2) and is contained in the ball of radius n + n(1/3)(ln n)(4).