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dc.contributor.authorGwynne, Ewain
dc.contributor.authorHolden, Nina
dc.contributor.authorMiller, Jason
dc.date.accessioned2020-11-01T16:04:32Z
dc.date.available2020-11-01T16:04:32Z
dc.date.issued2019-11-02
dc.date.submitted2016-04-25
dc.identifier.issn0178-8051
dc.identifier.others00440-019-00952-y
dc.identifier.other952
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/312312
dc.descriptionFunder: University of Cambridge
dc.description.abstractAbstract: We prove a formula relating the Hausdorff dimension of a deterministic Borel subset of R and the Hausdorff dimension of its image under a conformal map from the upper half-plane to a complementary connected component of an SLEκ curve for κ≠4. Our proof is based on the relationship between SLE and Liouville quantum gravity together with the one-dimensional KPZ formula of Rhodes and Vargas (ESAIM Probab Stat 15:358–371, 2011) and the KPZ formula of Gwynne et al. (Ann Probab, 2015). As an intermediate step we prove a KPZ formula which relates the Euclidean dimension of a subset of an SLEκ curve for κ∈(0, 4)∪(4, 8) and the dimension of the same set with respect to the γ-quantum natural parameterization of the curve induced by an independent Gaussian free field, γ=κ∧(4/κ).
dc.languageen
dc.publisherSpringer Berlin Heidelberg
dc.subjectArticle
dc.subjectSchramm-Loewner evolution
dc.subjectLiouville quantum gravity
dc.subjectKPZ formula
dc.subjectHausdorff dimension
dc.subjectConformal map
dc.subjectPeanosphere
dc.subject60J67
dc.titleDimension transformation formula for conformal maps into the complement of an SLE curve
dc.typeArticle
dc.date.updated2020-11-01T16:04:31Z
prism.endingPage667
prism.issueIdentifier1-2
prism.publicationNameProbability Theory and Related Fields
prism.startingPage649
prism.volume176
dc.identifier.doi10.17863/CAM.59406
rioxxterms.versionofrecord10.1007/s00440-019-00952-y
rioxxterms.versionVoR
rioxxterms.licenseref.urihttps://creativecommons.org/licenses/by/4.0/
dc.identifier.eissn1432-2064


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