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 Electronic Journal of Probability > Vol. 7 (2002) > Paper 16 open journal systems 


Phase Transition for the Frog Model

Oswaldo Alves, Universidade Federal de Goias
Fábio Machado, Universidade de São Paulo
Serguei Popov, Universidade de São Paulo


Abstract
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 $bbZ^d$ and regular trees.



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Pages: 1-21

Published on: May 16, 2002


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Electronic Journal of Probability. ISSN: 1083-6489