COVER TIME FOR THE FROG MODEL ON TREES

FORUM OF MATHEMATICS SIGMA, 2019.

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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(r...More

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