Frogs in random environment

We study the so-called frog model: Initially there are some "sleeping" part icles and one "active" particle. A sleeping particle is activated when an a ctive: particle hits it. after that the activated particle starts to walk i ndependently of everything and can activate other sleeping particles as wel l. The initial configuration of sleeping particles is random with density p (x). We identify the critical rate of decay of p(x) separating transience f rom recurrence, and study some other properties of the model.