Speed of Vertex reinforced jump process on Galton-Watson trees

Xinxin Chen (1) , Xiaolin Zeng (1)

1 PSPM - Probabilités, statistique, physique mathématique

We give an alternative proof of the fact that the vertex reinforced jump process on Galton-Watson tree has a phase transition between recurrence and transience as a function of c, the initial local time, see [3]. Further, applying techniques in [1], we show a phase transition between positive speed and null speed for the associated discrete time process in the transient regime.

Domaines: Probabilités [math.PR]

Xinxin Chen, Xiaolin Zeng. Speed of Vertex reinforced jump process on Galton-Watson trees. Journal of Theoretical Probability, 2018, 31 (2), pp.1166-1211. ⟨hal-01359591⟩