A note on the recurrence of edge reinforced random walks

Laurent Tournier (1)

1 ICJ - Institut Camille Jordan

We give a short proof of Theorem 2.1 from [MR07], stating that the linearly edge reinforced random walk (ERRW) on a locally finite graph is recurrent if and only if it returns to its starting point almost surely. This result was proved in [MR07] by means of the much stronger property that the law of the ERRW is a mixture of Markov chains. Our proof only uses this latter property on finite graphs, in which case it is a consequence of De Finetti's theorem on exchangeability.

Mots clés: random walks; edge reinforced random walk; recurrence; exchangeability; errw

Domaines: Probabilités [math.PR]

Laurent Tournier. A note on the recurrence of edge reinforced random walks. 2009. ⟨hal-00435424v2⟩