Show simple item record

dc.contributor.authorVargas, Vincent
HAL ID: 739861
dc.contributor.authorSheffield, Scott
dc.contributor.authorDuplantier, Bertrand
dc.contributor.authorRhodes, Rémi
dc.date.accessioned2012-12-05T15:38:47Z
dc.date.available2012-12-05T15:38:47Z
dc.date.issued2014
dc.identifier.issn0010-3616
dc.identifier.urihttps://basepub.dauphine.fr/handle/123456789/10693
dc.language.isoenen
dc.subjectKPZ
dc.subjectGaussian multiplicative chaos
dc.subjectLiouville quantum gravity
dc.subjectrenormalization
dc.subjectderivative martingale
dc.subject.ddc519en
dc.titleRenormalization of Critical Gaussian Multiplicative Chaos and KPZ relation
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.abstractenGaussian Multiplicative Chaos is a way to produce a measure on $\R^d$ (or subdomain of $\R^d$) of the form $e^{\gamma X(x)} dx$, where $X$ is a log-correlated Gaussian field and $\gamma \in [0,\sqrt{2d})$ is a fixed constant. A renormalization procedure is needed to make this precise, since $X$ oscillates between $-\infty$ and $\infty$ and is not a function in the usual sense. This procedure yields the zero measure when $\gamma=\sqrt{2d}$. Two methods have been proposed to produce a non-trivial measure when $\gamma=\sqrt{2d}$. The first involves taking a derivative at $\gamma=\sqrt{2d}$ (and was studied in an earlier paper by the current authors), while the second involves a modified renormalization scheme. We show here that the two constructions are equivalent and use this fact to deduce several quantitative properties of the random measure. In particular, we complete the study of the moments of the derivative martingale, which allows us to establish the KPZ formula at criticality.
dc.relation.isversionofjnlnameCommunications in Mathematical Physics
dc.relation.isversionofjnlvol330
dc.relation.isversionofjnlissue1
dc.relation.isversionofjnldate2014
dc.relation.isversionofjnlpages283-330
dc.relation.isversionofdoihttp://dx.doi.org/10.1007/s00220-014-2000-6
dc.identifier.urlsitehttps://hal.archives-ouvertes.fr/hal-00760405
dc.relation.isversionofjnlpublisherSpringer
dc.subject.ddclabelProbabilités et mathématiques appliquéesen
dc.description.submittednonen
dc.description.ssrncandidatenon
dc.description.halcandidateoui
dc.description.readershiprecherche
dc.description.audienceInternational
dc.relation.Isversionofjnlpeerreviewedoui
dc.date.updated2017-10-27T11:58:34Z


Files in this item

FilesSizeFormatView

There are no files associated with this item.

This item appears in the following Collection(s)

Show simple item record