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arXiv · 1710.05884

Infection spread for the frog model on trees

Christopher Hoffman·Tobias Johnson·Matthew Junge
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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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Christopher Hoffman, Tobias Johnson, Matthew Junge. 2017-10-16. Infection spread for the frog model on trees. https://doi.org/10.1214/19-ejp368

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