Electronic Journal of Probability

Infection spread for the frog model on trees

Christopher Hoffman, Tobias Johnson, and Matthew Junge

Full-text: Open access

Abstract

The frog model is an infection process in which dormant particles begin moving and infecting others once they become infected. We show that on the rooted $d$-ary tree with particle density $\Omega (d^{2})$, the set of visited sites contains a linearly expanding ball and the number of visits to the root grows linearly with high probability.

Article information

Source
Electron. J. Probab., Volume 24 (2019), paper no. 112, 29 pp.

Dates
Received: 5 August 2018
Accepted: 20 September 2019
First available in Project Euclid: 9 October 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejp/1570586692

Digital Object Identifier
doi:10.1214/19-EJP368

Subjects
Primary: 60K35: Interacting random processes; statistical mechanics type models; percolation theory [See also 82B43, 82C43] 60J80: Branching processes (Galton-Watson, birth-and-death, etc.) 60J10: Markov chains (discrete-time Markov processes on discrete state spaces)

Keywords
frog model phase transition

Rights
Creative Commons Attribution 4.0 International License.

Citation

Hoffman, Christopher; Johnson, Tobias; Junge, Matthew. Infection spread for the frog model on trees. Electron. J. Probab. 24 (2019), paper no. 112, 29 pp. doi:10.1214/19-EJP368. https://projecteuclid.org/euclid.ejp/1570586692


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