Continuous time vertex reinforced jump processes on Galton-Watson trees

Anne-Laure Basdevant (1) , Arvind Singh (2)

1 MODAL'X - Modélisation aléatoire de Paris X
2 LM-Orsay - Laboratoire de Mathématiques d'Orsay

We consider a continuous time vertex reinforced jump process on a supercritical Galton-Watson tree. This process takes values in the set of vertices of the tree and jumps to a neighbouring vertex with rate proportional to the local time at that vertex plus a constant. In this paper, we complete results previously obtained by Davis and Volkov (2002,2004) and Collevecchio (2006,2009) by providing a characterization for the recurrence/transience of the walk.

Mots clés: Reinforced processes; phase transition; random walks on trees; branching processes

Domaines: Probabilités [math.PR]

Anne-Laure Basdevant, Arvind Singh. Continuous time vertex reinforced jump processes on Galton-Watson trees. 2010. ⟨hal-00485046⟩