COVER TIME FOR THE FROG MODEL ON TREES

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 $\unicode[STIX]{x1D707}$ on the full $d$ -ary tree of height $n$ . If $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D6FA}(d^{2})$ , all of the vertices are visit...

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Bibliographic Details
Published in:Forum of mathematics. Sigma 2019-01, Vol.7, Article e41
Main Authors: HOFFMAN, CHRISTOPHER, JOHNSON, TOBIAS, JUNGE, MATTHEW
Format: Article
Language:English
Subjects:
60J10
60J80
60K35
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Summary: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 $\unicode[STIX]{x1D707}$ on the full $d$ -ary tree of height $n$ . If $\unicode[STIX]{x1D707}=\unicode[STIX]{x1D6FA}(d^{2})$ , all of the vertices are visited in time $\unicode[STIX]{x1D6E9}(n\log n)$ with high probability. Conversely, if $\unicode[STIX]{x1D707}=O(d)$ the cover time is $\exp (\unicode[STIX]{x1D6E9}(\sqrt{n}))$ with high probability.
ISSN:2050-5094
2050-5094
DOI:10.1017/fms.2019.37