dc.contributor.author Gwynne, Ewain en dc.contributor.author Miller, Jason en dc.contributor.author Qian, Wei en dc.date.accessioned 2019-11-09T00:30:40Z dc.date.available 2019-11-09T00:30:40Z dc.identifier.issn 1073-7928 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/298774 dc.description.abstract The 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.publisher Oxford University Press dc.rights All rights reserved dc.rights.uri dc.title Conformal invariance of $\CLE_\kappa$ on the Riemann sphere for $\kappa \in (4,8)$ en dc.type Article prism.publicationName International Mathematics Research Notices en dc.identifier.doi 10.17863/CAM.45830 dcterms.dateAccepted 2019-11-07 en rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2019-11-07 en rioxxterms.type Journal Article/Review en rioxxterms.freetoread.startdate 2022-11-08
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