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The random pinning model with correlated disorder given by a renewal set

hal.structure.identifier
dc.contributor.authorCheliotis, Dimitris
hal.structure.identifier
dc.contributor.authorChino, Yuki
hal.structure.identifierCEntre de REcherches en MAthématiques de la DEcision [CEREMADE]
dc.contributor.authorPoisat, Julien
HAL ID: 6620
dc.date.accessioned2019-12-20T13:51:47Z
dc.date.available2019-12-20T13:51:47Z
dc.date.issued2019
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/20371
dc.language.isoenen
dc.subjectPinning modelen
dc.subjectlocalization transitionen
dc.subjectfree energyen
dc.subjectcorrelated disorderen
dc.subjectrenewalen
dc.subjectdisorder relevanceen
dc.subjectHarris criterionen
dc.subjectsmoothing inequalityen
dc.subjectsecond momenten
dc.subject.ddc519en
dc.titleThe random pinning model with correlated disorder given by a renewal seten
dc.typeArticle accepté pour publication ou publié
dc.description.abstractenWe investigate the effect of correlated disorder on the localization transition undergone by a renewal sequence with loop exponent α > 0, when the correlated sequence is given by another independent renewal set with loop exponent α > 0. Using the renewal structure of the disorder sequence, we compute the annealed critical point and exponent. Then, using a smoothing inequality for the quenched free energy and second moment estimates for the quenched partition function, combined with decoupling inequalities, we prove that in the case α > 2 (summable correlations), disorder is irrelevant if α < 1/2 and relevant if α > 1/2, which extends the Harris criterion for independent disorder. The case α ∈ (1, 2) (non-summable correlations) remains largely open, but we are able to prove that disorder is relevant for α > 1/ ˆ α, a condition that is expected to be non-optimal. Predictions on the criterion for disorder relevance in this case are discussed. Finally, the case α ∈ (0, 1) is somewhat special but treated for completeness: in this case, disorder has no effect on the quenched free energy, but the annealed model exhibits a phase transition.en
dc.relation.isversionofjnlnameAnnales Henri Lebesgue
dc.relation.isversionofjnlissue2en
dc.relation.isversionofjnldate2019-07
dc.relation.isversionofjnlpages281-329en
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-01590623v2en
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.Isversionofjnlpeerreviewednonen
dc.relation.Isversionofjnlpeerreviewednonen
dc.date.updated2019-12-20T13:48:16Z
hal.author.functionaut
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