INTERNAL DIFFUSION LIMITED AGGREGATION
成果类型：
Article
署名作者：
LAWLER, GF; BRAMSON, M; GRIFFEATH, D
署名单位：
University of Wisconsin System; University of Wisconsin Madison
刊物名称：
ANNALS OF PROBABILITY
ISSN/ISSBN：
0091-1798
DOI：
10.1214/aop/1176989542
发表日期：
1992
页码：
2117-2140
关键词：
摘要：
We study the asymptotic shape of the occupied region for an interacting lattice system proposed recently by Diaconis and Fulton. In this model particles are repeatedly dropped at the origin of the d-dimensional integers. Each successive particle then performs an independent simple random walk until it sticks at the first site not previously occupied. Our main theorem asserts that as the cluster of stuck particles grows, its shape approaches a Euclidean ball. The proof of this result involves Green's function asymptotics, duality and large deviation bounds. We also quantify the time scale of the model, establish close connections with a continuous-time variant and pose some challenging problems concerning more detailed aspects of the dynamics.