## Electronic Journal of Probability

### Infection spread for the frog model on trees

#### 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
Accepted: 20 September 2019
First available in Project Euclid: 9 October 2019

https://projecteuclid.org/euclid.ejp/1570586692

Digital Object Identifier
doi:10.1214/19-EJP368

Mathematical Reviews number (MathSciNet)
MR4017130

Zentralblatt MATH identifier
07142906

Keywords
frog model phase transition

#### 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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