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Infection spread for the frog model on trees

Christopher Hoffman,Tobias Johnson,Matthew Junge

ELECTRONIC JOURNAL OF PROBABILITY（2019）

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Abstract
The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted d-ary tree with particle density Omega(d(2)), the set of visited sites contains a linearly expanding ball and the number of visits to the root grows linearly with high probability.
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Key words
frog model,phase transition
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