Electronic Communications in Probability
- Electron. Commun. Probab.
- Volume 24 (2019), paper no. 29, 9 pp.
Sensitivity of the frog model to initial conditions
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.
Electron. Commun. Probab., Volume 24 (2019), paper no. 29, 9 pp.
Received: 10 September 2018
Accepted: 12 April 2019
First available in Project Euclid: 5 June 2019
Permanent link to this document
Digital Object Identifier
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)
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