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Cover time for the frog model on trees
Christopher Hoffman, Tobias Johnson, Matthew Junge · 2018-02-08 · via math.PR updates on arXiv.org

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 $μ$ on the full $d$-ary tree of height $n$. If $μ= Ω( d^2)$, all of the vertices are visited in time $Θ(n\log n)$ with high probability. Conversely, if $μ= O(d)$ the cover time is $\exp(Θ(\sqrt n))$ with high probability.

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