Phase Transition for the Frog Model

Oswaldo Alves (Universidade Federal de Goias)
Fabio Machado (Universidade de Sao Paulo)
Serguei Popov (Universidade de São Paulo)


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. 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.

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Pages: 1-21

Publication Date: May 16, 2002

DOI: 10.1214/EJP.v7-115


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