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dc.contributor.authorSabot, Christophe
dc.contributor.authorTarres, Pierre
dc.date.accessioned2018-02-12T15:35:26Z
dc.date.available2018-02-12T15:35:26Z
dc.date.issued2015
dc.identifier.issn1435-9855
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/17384
dc.language.isoenen
dc.subjectSigma modelen
dc.subjectVertex Reinforced Random Walksen
dc.subjectEdge Reinforced Random Walksen
dc.subject.ddc519en
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, is a random process that takes values in the vertex set of a graph G, which is more likely to cross edges it has visited before. We show that it can be interpreted as an annealed version of the Vertex-reinforced jump process (VRJP), conceived by Werner and first studied by Davis and Volkov (2002,2004), 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. This enables us to deduce that VRJP is recurrent in any dimension for large reinforcement, using a localisation result of Disertori and Spencer (2010).en
dc.relation.isversionofjnlnameJournal of the European Mathematical Society
dc.relation.isversionofjnlvol17en
dc.relation.isversionofjnlissue9en
dc.relation.isversionofjnldate2015-10
dc.relation.isversionofjnlpages2353–2378en
dc.relation.isversionofdoi10.4171/JEMS/559en
dc.relation.isversionofjnlpublisherEuropean Mathematical Societyen
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
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.updated2018-02-12T15:32:41Z
hal.person.labIds193738
hal.person.labIds60


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