The frog model on non-amenable trees

Marcus Michelen, Josh Rosenberg

Research output: Contribution to journalArticlepeer-review


We examine an interacting particle system on trees commonly referred to as the frog model. For its initial state, it begins with a single active particle at the root and i.i.d. Poiss(λ) many inactive particles at each non-root vertex. Active particles perform discrete time simple random walk and in the process activate any inactive particles they encounter. We show that for every non-amenable tree with bounded degree there exists a phase transition from transience to recurrence (with a non-trivial intermediate phase sometimes sandwiched in between) as λ varies.

Original languageEnglish
Article number49
JournalElectronic Journal of Probability
StatePublished - 2020
Externally publishedYes


  • Frog model
  • Interacting random walk
  • Non-amenable


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