Recurrence for the frog model with drift on Z

The frog model is a system of interacting random walks. We give a criterion for recurrence/transience for the frog model in a particular example. In our case, the underlying random walk is an asymmetric random walk on Z, and the starting configuration is i.i.d. We also show that in this example, the probability to visit the origin infinitely often satisfies a 0 − 1−law.