Abstract
We study the frog model on Zd with drift in dimension d≥2 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 d≥3. Our proofs make use of (refined) couplings with branching random walks for the transience, and with percolation for the recurrence.
Citation
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
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