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.
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