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arXiv · 1802.03428

Cover time for the frog model on trees

Christopher Hoffman·Tobias Johnson·Matthew Junge
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Abstract

The frog model is a branching random walk on a graph in which particles branch only at unvisited sites. Consider an initial particle density of $\mu$ on the full $d$-ary tree of height $n$. If $\mu= \Omega( d^2)$, all of the vertices are visited in time $\Theta(n\log n)$ with high probability. Conversely, if $\mu = O(d)$ the cover time is $\exp(\Theta(\sqrt n))$ with high probability.

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Christopher Hoffman, Tobias Johnson, Matthew Junge. 2018-02-07. Cover time for the frog model on trees. https://doi.org/10.1017/fms.2019.37

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