Transience of edge-reinforced random walk

Margherita Disertori (1) , Christophe Sabot (2, 3) , Pierre Tarres (4)

1 HCM - Hausdorff Center for Mathematics
2 ICJ - Institut Camille Jordan
3 PSPM - Probabilités, statistique, physique mathématique
4 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

We show transience of the edge-reinforced random walk for small reinforcement in dimension $d\ge3$. The argument adapts the proof of quasi-diffusive behaviour of the SuSy hyperbolic model for fixed conductances by Disertori, Spencer and Zirnbauer (2010), using the representation of edge-reinforced random walk as a mixture of vertex-reinforced jump processes (VRJP) with independent gamma conductances, and the interpretation of the limit law of VRJP as a supersymmetric (SuSy) hyperbolic sigma model developed by Sabot and Tarres (2012).

Mots clés: transience; sigma supersymmetric hyperbolic model; recurrence; delocalization; edge-reinforced random walk; vertex-reinforced jump process

Domaines: Probabilités [math.PR]

Margherita Disertori, Christophe Sabot, Pierre Tarres. Transience of edge-reinforced random walk. Communications in Mathematical Physics, 2015, ⟨10.1007/s00220-015-2392-y⟩. ⟨hal-00962331⟩