Electronic Communications in Probability

The critical density for the frog model is the degree of the tree

Tobias Johnson and Matthew Junge

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The frog model on the rooted $d$-ary tree changes from transient to recurrent as the number of frogs per site is increased. We prove that the location of this transition is on the same order as the degree of the tree.

Article information

Electron. Commun. Probab., Volume 21 (2016), paper no. 82, 12 pp.

Received: 28 July 2016
Accepted: 15 November 2016
First available in Project Euclid: 3 December 2016

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Zentralblatt MATH identifier

Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

frog model transience recurrence phase transition trees stochastic dominance

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Johnson, Tobias; Junge, Matthew. The critical density for the frog model is the degree of the tree. Electron. Commun. Probab. 21 (2016), paper no. 82, 12 pp. doi:10.1214/16-ECP29. https://projecteuclid.org/euclid.ecp/1480734227

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