RECURRENCE AND TRANSIENCE FOR THE FROG MODEL ON TREES

ANNALS OF PROBABILITY, pp. 2826.0-2854.0, 2017.

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Abstract:

The frog model is a growing system of random walks where a particle is added whenever a new site is visited. A longstanding open question is how often the root is visited on the infinite d-ary tree. We prove the model undergoes a phase transition, finding it recurrent for d = 2 and transient for d >= 5. Simulations suggest strong recurren...More

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