Open Access
2020 On transience of frogs on Galton–Watson trees
Sebastian Müller, Gundelinde Maria Wiegel
Electron. J. Probab. 25: 1-30 (2020). DOI: 10.1214/20-EJP558


We consider an interacting particle system, known as the frog model, on infinite Galton–Watson trees allowing offspring 0 and 1. The system starts with one awake particle (frog) at the root of the tree and a random number of sleeping particles at the other vertices. Awake frogs move according to simple random walk on the tree and as soon as they encounter sleeping frogs, those will wake up and move independently according to simple random walk. The frog model is called transient if there are almost surely only finitely many particles returning to the root. In this paper we prove a 0–1-law for transience of the frog model and show the existence of a transient phase for certain classes of Galton–Watson trees.


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Sebastian Müller. Gundelinde Maria Wiegel. "On transience of frogs on Galton–Watson trees." Electron. J. Probab. 25 1 - 30, 2020.


Received: 6 March 2020; Accepted: 18 November 2020; Published: 2020
First available in Project Euclid: 23 December 2020

Digital Object Identifier: 10.1214/20-EJP558

Primary: 60J10 , 60J85 , 60K35

Keywords: branching Markov chain , frog model , Recurrence and transience

Vol.25 • 2020
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