Mathematics > Probability
[Submitted on 7 Feb 2018 (v1), last revised 24 Sep 2019 (this version, v3)]
Title:Cover time for the frog model on trees
View PDFAbstract: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.
Submission history
From: Tobias Johnson [view email][v1] Wed, 7 Feb 2018 23:12:49 UTC (41 KB)
[v2] Wed, 14 Feb 2018 18:04:18 UTC (41 KB)
[v3] Tue, 24 Sep 2019 14:41:09 UTC (42 KB)
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