Open Access
2020 The initial set in the frog model is irrelevant
Maria Deijfen, Sebastian Rosengrenï
Electron. Commun. Probab. 25: 1-7 (2020). DOI: 10.1214/20-ECP329


In this note, we consider the frog model on $\mathbb {Z}^{d}$ and a two-type version of it with two types of particles. For the one-type model, we show that the asymptotic shape does not depend on the initially activated set and the configuration there. For the two-type model, we show that the possibility for the types to coexist in that both of them activate infinitely many particles does not depend on the choice of the initially activated sets and the configurations there.


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Maria Deijfen. Sebastian Rosengrenï. "The initial set in the frog model is irrelevant." Electron. Commun. Probab. 25 1 - 7, 2020.


Received: 20 December 2019; Accepted: 24 June 2020; Published: 2020
First available in Project Euclid: 23 July 2020

zbMATH: 07252770
Digital Object Identifier: 10.1214/20-ECP329

Primary: 60K35

Keywords: asymptotic shape , Coexistence , competing growth , frog model , Random walk

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