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2019 Sensitivity of the frog model to initial conditions
Tobias Johnson, Leonardo T. Rolla
Electron. Commun. Probab. 24: 1-9 (2019). DOI: 10.1214/19-ECP230


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.


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Tobias Johnson. Leonardo T. Rolla. "Sensitivity of the frog model to initial conditions." Electron. Commun. Probab. 24 1 - 9, 2019.


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

zbMATH: 07068653
MathSciNet: MR3962479
Digital Object Identifier: 10.1214/19-ECP230

Primary: 60J10 , 60J80 , 60K35

Keywords: Activated random walk , Branching random walk , frog model , recurrence , transience


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