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Phase Transition for the Frog Model
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Oswaldo Alves, Universidade Federal de Goias
Fábio Machado, Universidade de São Paulo
Serguei Popov, Universidade de São Paulo
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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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Full text: PDF
Pages: 1-21
Published on: May 16, 2002
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Electronic Journal of Probability. ISSN: 1083-6489 |
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Context