Open Access
June 2016 From transience to recurrence with Poisson tree frogs
Christopher Hoffman, Tobias Johnson, Matthew Junge
Ann. Appl. Probab. 26(3): 1620-1635 (June 2016). DOI: 10.1214/15-AAP1127


Consider the following interacting particle system on the $d$-ary tree, known as the frog model: Initially, one particle is awake at the root and i.i.d. Poisson many particles are sleeping at every other vertex. Particles that are awake perform simple random walks, awakening any sleeping particles they encounter. We prove that there is a phase transition between transience and recurrence as the initial density of particles increases, and we give the order of the transition up to a logarithmic factor.


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Christopher Hoffman. Tobias Johnson. Matthew Junge. "From transience to recurrence with Poisson tree frogs." Ann. Appl. Probab. 26 (3) 1620 - 1635, June 2016.


Received: 1 January 2015; Revised: 1 June 2015; Published: June 2016
First available in Project Euclid: 14 June 2016

zbMATH: 1345.60116
MathSciNet: MR3513600
Digital Object Identifier: 10.1214/15-AAP1127

Primary: 60J10 , 60J80 , 60K35

Keywords: frog model , phase transition , recurrence , transience

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.26 • No. 3 • June 2016
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