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dc.contributor.authorGwynne, Ewainen
dc.contributor.authorMiller, Jasonen
dc.date.accessioned2020-09-11T23:31:33Z
dc.date.available2020-09-11T23:31:33Z
dc.identifier.issn0246-0203
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/310201
dc.description.abstractFor $\gamma \in (0,2)$, $U\subset \BB C$, and an instance $h$ of the Gaussian free field (GFF) on $U$, the $\gamma$-Liouville quantum gravity (LQG) surface associated with $(U,h)$ is formally described by the Riemannian metric tensor $e^{\gamma h} (dx^2 + dy^2)$ on $U$. Previous work by the authors showed that one can define a canonical metric (distance function) $D_h$ on $U$ associated with a $\gamma$-LQG surface. We show that this metric is conformally covariant in the sense that it respects the coordinate change formula for $\gamma$-LQG surfaces. That is, if $U,\widetilde{U}$ are domains, $\phi \colon U \to \widetilde{U}$ is a conformal transformation, $Q=2/\gamma+\gamma/2$, and $\widetilde h = h\circ\phi^{-1} + Q\log|(\phi^{-1})'|$, then $D_h(z,w) = D_{\widetilde{h}}(\phi(z),\phi(w))$ for all $z,w \in U$. This proves that $D_h$ is intrinsic to the quantum surface structure of $(U,h)$, i.e., it does not depend on the particular choice of parameterization.
dc.publisherInstitute of Mathematical Statistics
dc.rightsAll rights reserved
dc.rights.uri
dc.titleConformal covariance of the Liouville quantum gravity metricen
dc.typeArticle
prism.publicationNameL'Institut Henri Poincare, Annales B: Probabilites et Statistiquesen
dc.identifier.doi10.17863/CAM.57287
dcterms.dateAccepted2020-09-09en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2020-09-09en
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEuropean Commission Horizon 2020 (H2020) ERC (804166)
cam.orpheus.counter21*
rioxxterms.freetoread.startdate2023-09-11


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