Electronic Communications in Probability

Sensitivity of the frog model to initial conditions

Tobias Johnson and Leonardo T. Rolla

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Abstract

The frog model is an interacting particle system on a graph. Active particles perform independent simple random walks, while sleeping particles remain inert until visited by an active particle. Some number of sleeping particles are placed at each site sampled independently from a certain distribution, and then one particle is activated to begin the process. We show that the recurrence or transience of the model is sensitive not just to the expectation but to the entire distribution. This is in contrast to closely related models like branching random walk and activated random walk.

Article information

Source
Electron. Commun. Probab., Volume 24 (2019), paper no. 29, 9 pp.

Dates
Received: 10 September 2018
Accepted: 12 April 2019
First available in Project Euclid: 5 June 2019

Permanent link to this document
https://projecteuclid.org/euclid.ecp/1559700465

Digital Object Identifier
doi:10.1214/19-ECP230

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 recurrence transience branching random walk activated random walk

Rights
Creative Commons Attribution 4.0 International License.

Citation

Johnson, Tobias; Rolla, Leonardo T. Sensitivity of the frog model to initial conditions. Electron. Commun. Probab. 24 (2019), paper no. 29, 9 pp. doi:10.1214/19-ECP230. https://projecteuclid.org/euclid.ecp/1559700465


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References

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