dc.contributor.author Gwynne, Ewain dc.contributor.author Holden, Nina dc.contributor.author Miller, Jason dc.date.accessioned 2020-11-01T16:04:32Z dc.date.available 2020-11-01T16:04:32Z dc.date.issued 2019-11-02 dc.date.submitted 2016-04-25 dc.identifier.issn 0178-8051 dc.identifier.other s00440-019-00952-y dc.identifier.other 952 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/312312 dc.description Funder: University of Cambridge dc.description.abstract Abstract: 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.language en dc.publisher Springer Berlin Heidelberg dc.subject Article dc.subject Schramm-Loewner evolution dc.subject Liouville quantum gravity dc.subject KPZ formula dc.subject Hausdorff dimension dc.subject Conformal map dc.subject Peanosphere dc.subject 60J67 dc.title Dimension transformation formula for conformal maps into the complement of an SLE curve dc.type Article dc.date.updated 2020-11-01T16:04:31Z prism.endingPage 667 prism.issueIdentifier 1-2 prism.publicationName Probability Theory and Related Fields prism.startingPage 649 prism.volume 176 dc.identifier.doi 10.17863/CAM.59406 rioxxterms.versionofrecord 10.1007/s00440-019-00952-y rioxxterms.version VoR rioxxterms.licenseref.uri https://creativecommons.org/licenses/by/4.0/ dc.identifier.eissn 1432-2064
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