Phase transition for the frog model

O. S. M. Alves, F. P. Machado, S. Yu. Popov

Published 2001-04-03, updated 2001-07-03Version 2

We study a system of simple random walks on graphs, known as frog model. This model can be described as follows: There are active and sleeping particles living on some graph G. Each active particle performs a simple random walk with discrete time and at each moment it may disappear with probability 1-p. When an active particle hits a sleeping particle, the latter becomes active. Phase transition results and asymptotic values for critical parameters are presented for Z^d and regular trees.