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Open Access
2018 Recurrence and transience of frogs with drift on Zd
Christian Döbler, Nina Gantert, Thomas Höfelsauer, Serguei Popov, Felizitas Weidner
Electron. J. Probab. 23: 1-23 (2018). DOI: 10.1214/18-EJP216

Abstract

We study the frog model on Zd with drift in dimension d2 and establish the existence of transient and recurrent regimes depending on the transition probabilities. We focus on a model in which the particles perform nearest neighbour random walks which are balanced in all but one direction. This gives a model with two parameters. We present conditions on the parameters for recurrence and transience, revealing interesting differences between dimension d=2 and dimension d3. Our proofs make use of (refined) couplings with branching random walks for the transience, and with percolation for the recurrence.

Citation

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Christian Döbler. Nina Gantert. Thomas Höfelsauer. Serguei Popov. Felizitas Weidner. "Recurrence and transience of frogs with drift on Zd." Electron. J. Probab. 23 1 - 23, 2018. https://doi.org/10.1214/18-EJP216

Information

Received: 1 September 2017; Accepted: 22 August 2018; Published: 2018
First available in Project Euclid: 12 September 2018

zbMATH: 06964782
MathSciNet: MR3858916
Digital Object Identifier: 10.1214/18-EJP216

Subjects:
Primary: 60J10 , 60K35
Secondary: 60J80

Keywords: Branching random walk , frog model , Interacting random walks , percolation , recurrence , transience

Vol.23 • 2018
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