The shape theorem for the frog model with random initial configuration

Details The shape theorem for the frog model with random initial configuration The shape theorem for the frog model with random initial configuration

2001-10-25

arxiv.org/abs/math/0110280v1

Mathematics

Probability

Scientific paper

We prove a shape theorem for a growing set of simple random walks on Z^d, known as 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, the former becomes active as well. Initially, a random number of particles is placed into each site. At time 0 all particles are sleeping, except for those placed at the origin. We prove that the set of all sites visited by active particles, rescaled by the elapsed time, converges to a compact convex set.

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