Open Access
2020 The frog model on non-amenable trees
Marcus Michelen, Josh Rosenberg
Electron. J. Probab. 25: 1-16 (2020). DOI: 10.1214/20-EJP454


We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. $\mathrm{Poiss} (\lambda )$ many inactive particles at each non-root vertex. Active particles perform discrete time simple random walk and in the process activate any inactive particles they encounter. We show that for every non-amenable tree with bounded degree there exists a phase transition from transience to recurrence (with a non-trivial intermediate phase sometimes sandwiched in between) as $\lambda $ varies.


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Marcus Michelen. Josh Rosenberg. "The frog model on non-amenable trees." Electron. J. Probab. 25 1 - 16, 2020.


Received: 8 November 2019; Accepted: 7 April 2020; Published: 2020
First available in Project Euclid: 28 April 2020

zbMATH: 1441.60084
MathSciNet: MR4092768
Digital Object Identifier: 10.1214/20-EJP454

Primary: 60K35

Keywords: frog model , interacting random walk , non-amenable

Vol.25 • 2020
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