From transience to recurrence with Poisson tree frogs

Abstract

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.

Published at http://dx.doi.org/10.1214/15-AAP1127 in the Annals of Applied Probability (http://www.imstat.org/aap/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Recurrence for the frog model with drift on ${\mathbb{Z}}^d$
• The contact process on finite homogeneous trees revisited
• On the range of the transient frog model on Z

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