Recurrence and transience of frogs with drift on ℤ^d

We study the frog model on ℤ^d 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.