Open Access
2019 The frog model on trees with drift
Erin Beckman, Natalie Frank, Yufeng Jiang, Matthew Junge, Si Tang
Electron. Commun. Probab. 24: 1-10 (2019). DOI: 10.1214/19-ECP235


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.


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Erin Beckman. Natalie Frank. Yufeng Jiang. Matthew Junge. Si Tang. "The frog model on trees with drift." Electron. Commun. Probab. 24 1 - 10, 2019.


Received: 16 August 2018; Accepted: 18 April 2019; Published: 2019
First available in Project Euclid: 1 June 2019

zbMATH: 1422.60156
MathSciNet: MR3962476
Digital Object Identifier: 10.1214/19-ECP235

Primary: 60J10 , 60J80 , 60K35

Keywords: coupling , frog model , Interacting particle system , recurrence

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