The Frog Model on Trees

Опубликовано 22 июня 2016, 18:27

The frog model is a branching random walk that splits into two particles upon the first visit to each site. We prove a phase transition from recurrence to transience on the rooted d-ary tree. For d=2 the root is a.s. visited infinitely often and for d>4 only finitely often. This covers all but two cases of one of the longest standing open problems for this model. We conjecture the ternary tree remains recurrent while the quadrary tree is transient. This work is joint with Christopher Hoffman, Tobias Johnson and Matthew Junge.