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dc.contributor.authorMiller, Jason E.
dc.contributor.authorSheffield, Scott Roger
dc.date.accessioned2020-08-05T20:45:34Z
dc.date.available2020-08-05T20:45:34Z
dc.date.issued2019-08
dc.identifier.issn0246-0203
dc.identifier.urihttps://hdl.handle.net/1721.1/126480
dc.description.abstractWe show that the unit area Liouville quantum gravity sphere can be constructed in two equivalent ways. The first, which was introduced by the authors and Duplantier in (Liouville quantum gravity as a mating of trees (2014) Preprint), uses a Bessel excursion measure to produce a Gaussian free field variant on the cylinder. The second uses a correlated Brownian loop and a "mating of trees" to produce a Liouville quantum gravity sphere decorated by a space-filling path. In the special case that γ = √8/3, we present a third equivalent construction, which uses the excursion measure of a 3/2-stable Levy process (with only upward jumps) to produce a pair of trees of quantum disks that can be mated to produce a sphere decorated by SLE6. This construction is relevant to a program for showing that the γ =√8/3 Liouville quantum gravity sphere is equivalent to the Brownian map.en_US
dc.description.sponsorshipDivision of Mathematical Sciences (Awards DMS-1204894, DMS-1209044)en_US
dc.description.sponsorshipEPSRC (Grants EP-L018896-1, EP-I03372X-1)en_US
dc.language.isoen
dc.publisherInstitute of Mathematical Statisticsen_US
dc.relation.isversionofhttp://dx.doi.org/10.1214/18-aihp932en_US
dc.rightsCreative Commons Attribution-Noncommercial-Share Alikeen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/4.0/en_US
dc.sourcearXiven_US
dc.titleLiouville quantum gravity spheres as matings of finite-diameter treesen_US
dc.typeArticleen_US
dc.identifier.citationMiller, Jason and Scott Sheffield. "Liouville quantum gravity spheres as matings of finite-diameter trees." Annales de l'Institut Henri Poincaré, Probabilités et Statistiques 55, 3 (August 2019): 1712-1750 © 2019 Association des Publications de l'Institut Henri Poincaréen_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.relation.journalAnnales de l'Institut Henri Poincaré, Probabilités et Statistiquesen_US
dc.eprint.versionAuthor's final manuscripten_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2019-11-19T19:40:46Z
dspace.date.submission2019-11-19T19:40:51Z
mit.journal.volume55en_US
mit.journal.issue3en_US
mit.metadata.statusComplete


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