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Transience of Edge-Reinforced Random Walk

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Date
2015
Link to item file
https://arxiv.org/abs/1403.6079v2
Dewey
Sciences connexes (physique, astrophysique)
Sujet
edge-reinforced random walk
Journal issue
Communications in Mathematical Physics
Volume
339
Number
1
Publication date
2015
Article pages
121-148
Publisher
Springer
DOI
http://dx.doi.org/10.1007/s00220-015-2392-y
URI
https://basepub.dauphine.fr/handle/123456789/16396
Collections
  • CEREMADE : Publications
Metadata
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Author
Disertori, Margherita
Sabot, Christophe
Tarres, Pierre
Type
Article accepté pour publication ou publié
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).

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