Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 26, 10 pp.
The frog model on trees with drift
We provide a uniform upper bound on the minimal drift so that the one-per-site frog model on a $d$-ary tree is recurrent. To do this, we introduce a subprocess that couples across trees with different degrees. Finding couplings for frog models on nested sequences of graphs is known to be difficult. The upper bound comes from combining the coupling with a new, simpler proof that the frog model on a binary tree is recurrent when the drift is sufficiently strong. Additionally, we describe a coupling between frog models on trees for which the degree of the smaller tree divides that of the larger one. This implies that the critical drift has a limit as $d$ tends to infinity along certain subsequences.
Electron. Commun. Probab., Volume 24 (2019), paper no. 26, 10 pp.
Received: 16 August 2018
Accepted: 18 April 2019
First available in Project Euclid: 1 June 2019
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)
Beckman, Erin; Frank, Natalie; Jiang, Yufeng; Junge, Matthew; Tang, Si. The frog model on trees with drift. Electron. Commun. Probab. 24 (2019), paper no. 26, 10 pp. doi:10.1214/19-ECP235. https://projecteuclid.org/euclid.ecp/1559354659