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dc.contributor.authorDuplantier, Bertrand
dc.contributor.authorRhodes, Rémi
dc.contributor.authorSheffield, Scott
dc.contributor.authorVargas, Vincent
dc.date.accessioned2012-07-11T13:50:38Z
dc.date.available2012-07-11T13:50:38Z
dc.date.issued2014
dc.identifier.issn0091-1798
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/9720
dc.language.isoenen
dc.subjectmultiplicative chaos
dc.subjectscale invariance
dc.subjectkpz
dc.subjectstar equation
dc.subjectrandom measure
dc.subject.ddc519en
dc.titleCritical Gaussian Multiplicative Chaos: Convergence of the Derivative Martingale
dc.typeArticle accepté pour publication ou publié
dc.contributor.editoruniversityotherMassachusets Institute of Technology (MIT);États-Unis
dc.contributor.editoruniversityotherInstitut de Physique Théorique (ex SPhT) (IPHT) http://www-spht.cea.fr/fr/ CNRS : URA2306 – CEA : DSM/IPHT;France
dc.description.abstractenIn this paper, we study Gaussian multiplicative chaos in the critical case. We show that the so-called derivative martingale, introduced in the context of branching Brownian motions and branching random walks, converges almost surely (in all dimensions) to a random measure with full support. We also show that the limiting measure has no atom. In connection with the derivative martingale, we write explicit conjectures about the glassy phase of log-correlated Gaussian potentials and the relation with the asymptotic expansion of the maximum of log-correlated Gaussian random variables.
dc.relation.isversionofjnlnameAnnals of Probability
dc.relation.isversionofjnlvol42
dc.relation.isversionofjnlissue5
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages1769-1808
dc.relation.isversionofdoi10.1214/13-AOP890
dc.identifier.urlsitehttps://arxiv.org/abs/1206.1671v3
dc.description.sponsorshipprivateouien
dc.relation.isversionofjnlpublisherInstitute of Mathematical Statistics
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.relation.forthcomingoui
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dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2016-12-03T14:49:56Z


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