The Annals of Applied Probability
- Ann. Appl. Probab.
- Volume 26, Number 3 (2016), 1620-1635.
From transience to recurrence with Poisson tree frogs
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.
Ann. Appl. Probab., Volume 26, Number 3 (2016), 1620-1635.
Received: January 2015
Revised: June 2015
First available in Project Euclid: 14 June 2016
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
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)
Hoffman, Christopher; Johnson, Tobias; Junge, Matthew. From transience to recurrence with Poisson tree frogs. Ann. Appl. Probab. 26 (2016), no. 3, 1620--1635. doi:10.1214/15-AAP1127. https://projecteuclid.org/euclid.aoap/1465905013