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- W2964156105 abstract "We show transience of the edge-reinforced random walk (ERRW) for small reinforcement in dimension $${dge3}$$ . 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)." @default.
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- W2964156105 date "2015-06-10" @default.
- W2964156105 modified "2023-09-30" @default.
- W2964156105 title "Transience of Edge-Reinforced Random Walk" @default.
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- W2964156105 doi "https://doi.org/10.1007/s00220-015-2392-y" @default.
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