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Edge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma model

hal.structure.identifier
dc.contributor.authorSabot, Christophe
HAL ID: 16397
hal.structure.identifier
dc.contributor.authorTarres, Pierre
dc.date.accessioned2017-03-18T10:30:02Z
dc.date.available2017-03-18T10:30:02Z
dc.date.issued2015
dc.identifier.issn1435-9855
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/16388
dc.language.isoenen
dc.subjectSelf-interacting random walken
dc.subjectreinforcementen
dc.subjectrandom walk in random environmenten
dc.subjectsigma modelsen
dc.subjectsupersymmetryen
dc.subjectde Finetti theoremen
dc.subject.ddc520en
dc.titleEdge-reinforced random walk, vertex-reinforced jump process and the supersymmetric hyperbolic sigma modelen
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenEdge-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.isversionofjnlnameJournal of the European Mathematical Society
dc.relation.isversionofjnlvol17en
dc.relation.isversionofjnlissue9en
dc.relation.isversionofjnldate2015
dc.relation.isversionofjnlpages2353-2378en
dc.relation.isversionofdoi10.4171/JEMS/559en
dc.identifier.urlsitehttps://arxiv.org/abs/1111.3991v4en
dc.relation.isversionofjnlpublisherSpringeren
dc.subject.ddclabelSciences connexes (physique, astrophysique)en
dc.relation.forthcomingnonen
dc.relation.forthcomingprintnonen
dc.description.ssrncandidatenonen
dc.description.halcandidatenonen
dc.description.readershiprechercheen
dc.description.audienceInternationalen
dc.relation.Isversionofjnlpeerreviewedouien
dc.relation.Isversionofjnlpeerreviewedouien
dc.date.updated2017-03-13T13:27:10Z
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