The shape theorem for the frog model
成果类型：
Article
署名作者：
Alves, OSM; Machado, FP; Popov, SY
署名单位：
Universidade de Sao Paulo
刊物名称：
ANNALS OF APPLIED PROBABILITY
ISSN/ISSBN：
1050-5164
发表日期：
2002
页码：
533-546
关键词：
摘要：
We prove a shape theorem for a growing set of simple random walks on Z(d), known as the frog model. The dynamics of this process is described as follows: There are active particles, which perform independent discrete time SRWs, and sleeping particles, which do not move. When a sleeping particle is hit by an active particle, it becomes active too. At time 0 all particles are sleeping, except for that placed at the origin. We prove that the set of the original positions of all active particles, rescaled by the elapsed time, converges to some compact convex set.