From transience to recurrence with Poisson tree frogs
Probability
2016-06-23 v3
Abstract
Consider the following interacting particle system on the -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.
Cite
@article{arxiv.1501.05874,
title = {From transience to recurrence with Poisson tree frogs},
author = {Christopher Hoffman and Tobias Johnson and Matthew Junge},
journal= {arXiv preprint arXiv:1501.05874},
year = {2016}
}
Comments
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)