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Probabilidade e Combinatória

The branching-ruin number and the once-reinforced random walk
Daniel Kious

NYU Shanghai
Quarta-feira, 3 de outubro de 2018, 15:30
Sala 333

In a joint-work with Andrea Collevecchio and Vladas Sidoravicius, we study the phase transition for recurrence/transience of a class of self-interacting random walks on trees, which includes the once-reinforced random walk. For this purpose, we define a quantity, that we call the branching-ruin number of a tree, which provides - in the spirit of Furstenberg (1970) and Lyons (1990) - a natural way to measure trees with polynomial growth. We prove that the branching-ruin number of a tree is equal to the critical parameter for the recurrence/transience of the once-reinforced random walk. We define a sharp and effective (i.e. computable) criterion characterizing the recurrence/transience of a larger class of self-interacting walks on trees, providing the complete picture for their phase transition.