Electronic Journal of Probability

The frog model on non-amenable trees

Marcus Michelen and Josh Rosenberg

Full-text: Open access

Abstract

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.

Article information

Source
Electron. J. Probab., Volume 25 (2020), paper no. 49, 16 pp.

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

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1588039468

Digital Object Identifier
doi:10.1214/20-EJP454

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43]

Keywords
frog model non-amenable interacting random walk

Rights
Creative Commons Attribution 4.0 International License.

Citation

Michelen, Marcus; Rosenberg, Josh. The frog model on non-amenable trees. Electron. J. Probab. 25 (2020), paper no. 49, 16 pp. doi:10.1214/20-EJP454. https://projecteuclid.org/euclid.ejp/1588039468


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