The frog model is an interacting particle system modeling
spread of an infection in a moving population, among other things. It
can also be viewed as a model of dependent, directed percolation.
We show that the model exhibits a phase transition on several classes of
transitive graphs, including polynomial growth and non-amenable graphs.
We further show that the phase transition is sharp.
Joint work with Jonathan Hermon, Daniel de la Riva Massaad, and Yuliang Shi.