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dc.contributor.authorGwynne, Ewainen
dc.contributor.authorMiller, Jasonen
dc.contributor.authorQian, Weien
dc.date.accessioned2019-11-09T00:30:40Z
dc.date.available2019-11-09T00:30:40Z
dc.identifier.issn1073-7928
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/298774
dc.description.abstractThe conformal loop ensemble ($\CLE$) is the canonical conformally invariant probability measure on non-crossing loops in a simply connected domain in $\BB C$ and is indexed by a parameter $\kappa \in (8/3,8)$. We consider $\CLE_\kappa$ on the whole-plane in the regime in which the loops are self-intersecting ($\kappa \in (4,8)$) and show that it is invariant under the inversion map $z \mapsto 1/z$. This shows that whole-plane $\CLE_\kappa$ for $\kappa \in (4,8)$ defines a conformally invariant measure on loops on the Riemann sphere. The analogous statement in the regime in which the loops are simple ($\kappa \in (8/3,4]$) was proven by Kemppainen and Werner and together with the present work covers the entire range $\kappa \in (8/3,8)$ for which $\CLE_\kappa$ is defined. As an intermediate step in the proof, we show that $\CLE_\kappa$ for $\kappa \in (4,8)$ on an annulus, with any specified number of inner-boundary-surrounding loops, is well-defined and conformally invariant.
dc.publisherOxford University Press
dc.rightsAll rights reserved
dc.rights.uri
dc.titleConformal invariance of $\CLE_\kappa$ on the Riemann sphere for $\kappa \in (4,8)$en
dc.typeArticle
prism.publicationNameInternational Mathematics Research Noticesen
dc.identifier.doi10.17863/CAM.45830
dcterms.dateAccepted2019-11-07en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2019-11-07en
rioxxterms.typeJournal Article/Reviewen
rioxxterms.freetoread.startdate2022-11-08


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