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 $Z^d$ and regular trees.
Citation
Oswaldo Alves. Fabio Machado. Serguei Popov. "Phase Transition for the Frog Model." Electron. J. Probab. 7 1 - 21, 2002. https://doi.org/10.1214/EJP.v7-115
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