| dc.contributor.author | Sabot, Christophe | |
| dc.contributor.author | Tarres, Pierre | |
| dc.date.accessioned | 2017-03-18T10:30:02Z | |
| dc.date.available | 2017-03-18T10:30:02Z | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 1435-9855 | |
| dc.identifier.uri | https://basepub.dauphine.fr/handle/123456789/16388 | |
| dc.language.iso | en | en |
| dc.subject | Self-interacting random walk | en |
| dc.subject | reinforcement | en |
| dc.subject | random walk in random environment | en |
| dc.subject | sigma models | en |
| dc.subject | supersymmetry | en |
| dc.subject | de Finetti theorem | en |
| dc.subject.ddc | 520 | en |
| dc.title | Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model | en |
| dc.type | Article accepté pour publication ou publié | |
| dc.description.abstracten | Edge-reinforced random walk (ERRW), introduced by Coppersmith and Diaconis in 1986 [8], is a random process which takes values in the vertex set of a graph G and is more likely to cross edges it has visited before. We show that it can be represented in terms of a vertex-reinforced jump process (VRJP) with independent gamma conductances; the VRJP was conceived by Werner and first studied by Davis and Volkov [10, 11], and is a continuous-time process favouring sites with more local time. We calculate, for any finite graph G, the limiting measure of the centred occupation time measure of VRJP, and interpret it as a supersymmetric hyperbolic sigma model in quantum field theory, introduced by Zirnbauer in 1991 [35].This enables us to deduce that VRJP and ERRWare positive recurrent on any graph of bounded degree for large reinforcement, and that the VRJP is transient on Zd,d≥3, for small reinforcement, using results of Disertori and Spencer [15] and Disertori, Spencer and Zirnbauer [16]. | en |
| dc.relation.isversionofjnlname | Journal of the European Mathematical Society | |
| dc.relation.isversionofjnlvol | 17 | en |
| dc.relation.isversionofjnlissue | 9 | en |
| dc.relation.isversionofjnldate | 2015 | |
| dc.relation.isversionofjnlpages | 2353-2378 | en |
| dc.relation.isversionofdoi | 10.4171/JEMS/559 | en |
| dc.identifier.urlsite | https://arxiv.org/abs/1111.3991v4 | en |
| dc.relation.isversionofjnlpublisher | Springer | en |
| dc.subject.ddclabel | Sciences connexes (physique, astrophysique) | en |
| dc.relation.forthcoming | non | en |
| dc.relation.forthcomingprint | non | en |
| dc.description.ssrncandidate | non | en |
| dc.description.halcandidate | non | en |
| dc.description.readership | recherche | en |
| dc.description.audience | International | en |
| dc.relation.Isversionofjnlpeerreviewed | oui | en |
| dc.relation.Isversionofjnlpeerreviewed | oui | en |
| dc.date.updated | 2017-03-13T13:27:10Z | |
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