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dc.contributor.authorMiller, Jason
dc.contributor.authorSheffield, Scott
dc.date.accessioned2021-04-10T15:24:32Z
dc.date.available2021-04-10T15:24:32Z
dc.date.issued2021-03-25
dc.date.submitted2017-05-09
dc.identifier.issn0178-8051
dc.identifier.others00440-021-01026-8
dc.identifier.other1026
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/319705
dc.description.abstractAbstract: Previous works in this series have shown that an instance of a 8/3-Liouville quantum gravity (LQG) sphere has a well-defined distance function, and that the resulting metric measure space (mm-space) agrees in law with the Brownian map (TBM). In this work, we show that given just the mm-space structure, one can a.s. recover the LQG sphere. This implies that there is a canonical way to parameterize an instance of TBM by the Euclidean sphere (up to Möbius transformation). In other words, an instance of TBM has a canonical conformal structure. The conclusion is that TBM and the 8/3-LQG sphere are equivalent. They ultimately encode the same structure (a topological sphere with a measure, a metric, and a conformal structure) and have the same law. From this point of view, the fact that the conformal structure a.s. determines the metric and vice-versa can be understood as a property of this unified law. The results of this work also imply that the analogous facts hold for Brownian and 8/3-LQG surfaces with other topologies.
dc.languageen
dc.publisherSpringer Berlin Heidelberg
dc.subjectArticle
dc.subject60D05
dc.subject60J67
dc.titleLiouville quantum gravity and the Brownian map III: the conformal structure is determined
dc.typeArticle
dc.date.updated2021-04-10T15:24:32Z
prism.endingPage1211
prism.issueIdentifier3-4
prism.publicationNameProbability Theory and Related Fields
prism.startingPage1183
prism.volume179
dc.identifier.doi10.17863/CAM.66826
dcterms.dateAccepted2020-12-01
rioxxterms.versionofrecord10.1007/s00440-021-01026-8
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.contributor.orcidSheffield, Scott [0000-0002-5951-4933]
dc.identifier.eissn1432-2064


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