Transience of Edge-Reinforced Random Walk
Disertori, Margherita; Sabot, Christophe; Tarres, Pierre (2015), Transience of Edge-Reinforced Random Walk, Communications in Mathematical Physics, 339, 1, p. 121-148. 10.1007/s00220-015-2392-y
TypeArticle accepté pour publication ou publié
External document linkhttps://arxiv.org/abs/1403.6079v2
Journal nameCommunications in Mathematical Physics
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Abstract (EN)We show transience of the edge-reinforced random walk (ERRW) for small reinforcement in dimension d≥3. This proves the existence of a phase transition between recurrent and transient behavior, thus solving an open problem stated by Diaconis in 1986. The argument adapts the proof of quasi-diffusive behavior of the supersymmetric (SuSy) hyperbolic model for fixed conductances by Disertori et al. (Commun Math Phys 300:435–486, 2010), using the representation of ERRW as a mixture of vertex-reinforced jump processes (VRJP) with independent gamma conductances, and the interpretation of the limit law of VRJP as a SuSy hyperbolic sigma model developed by Sabot and Tarrès (J Eur Math Soc, arXiv:1111.3991, 2015).
Subjects / Keywordsedge-reinforced random walk
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