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Article Dans Une Revue Communications in Mathematical Physics Année : 2015

Transience of edge-reinforced random walk

Résumé

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).
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Dates et versions

hal-00962331 , version 1 (21-03-2014)

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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⟩
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