dc.contributor.author Vargas, Vincent HAL ID: 739861 dc.contributor.author Sheffield, Scott dc.contributor.author Duplantier, Bertrand dc.contributor.author Rhodes, Rémi dc.date.accessioned 2012-12-05T15:38:47Z dc.date.available 2012-12-05T15:38:47Z dc.date.issued 2014 dc.identifier.issn 0010-3616 dc.identifier.uri https://basepub.dauphine.fr/handle/123456789/10693 dc.language.iso en en dc.subject KPZ dc.subject Gaussian multiplicative chaos dc.subject Liouville quantum gravity dc.subject renormalization dc.subject derivative martingale dc.subject.ddc 519 en dc.title Renormalization of Critical Gaussian Multiplicative Chaos and KPZ relation dc.type Article accepté pour publication ou publié dc.contributor.editoruniversityother Massachusets Institute of Technology (MIT);États-Unis dc.contributor.editoruniversityother Institut de Physique Théorique (ex SPhT) (IPHT) http://www-spht.cea.fr/fr/ CNRS : URA2306 – CEA : DSM/IPHT;France dc.description.abstracten Gaussian 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.isversionofjnlname Communications in Mathematical Physics dc.relation.isversionofjnlvol 330 dc.relation.isversionofjnlissue 1 dc.relation.isversionofjnldate 2014 dc.relation.isversionofjnlpages 283-330 dc.relation.isversionofdoi http://dx.doi.org/10.1007/s00220-014-2000-6 dc.identifier.urlsite https://hal.archives-ouvertes.fr/hal-00760405 dc.relation.isversionofjnlpublisher Springer dc.subject.ddclabel Probabilités et mathématiques appliquées en dc.description.submitted non en dc.description.ssrncandidate non dc.description.halcandidate oui dc.description.readership recherche dc.description.audience International dc.relation.Isversionofjnlpeerreviewed oui dc.date.updated 2017-10-27T11:58:34Z
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