## Electronic Communications in Probability

### The frog model on trees with drift

#### Abstract

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.

#### Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 26, 10 pp.

Dates
Accepted: 18 April 2019
First available in Project Euclid: 1 June 2019

https://projecteuclid.org/euclid.ecp/1559354659

Digital Object Identifier
doi:10.1214/19-ECP235

Mathematical Reviews number (MathSciNet)
MR3962476

Zentralblatt MATH identifier
1422.60156

#### Citation

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

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