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dc.contributor.authorMiller, Jason P.
dc.contributor.authorSheffield, Scott Roger
dc.date.accessioned2016-10-20T20:18:53Z
dc.date.available2016-10-20T20:18:53Z
dc.date.issued2016-03
dc.date.submitted2016-02
dc.identifier.issn0178-8051
dc.identifier.issn1432-2064
dc.identifier.urihttp://hdl.handle.net/1721.1/104896
dc.description.abstractFix constants and θ∈[0,2π), and let h be an instance of the Gaussian free field on a planar domain. We study flow lines of the vector field e[superscript i(h/χ+θ)] starting at a fixed boundary point of the domain. Letting θ vary, one obtains a family of curves that look locally like SLE[subscript κ] processes with κ∈(0,4) (where χ=2[sqrt]κ−[sqrt]κ2), which we interpret as the rays of a random geometry with purely imaginary curvature. We extend the fundamental existence and uniqueness results about these paths to the case that the paths intersect the boundary. We also show that flow lines of different angles cross each other at most once but (in contrast to what happens when h is smooth) may bounce off of each other after crossing. Flow lines of the same angle started at different points merge into each other upon intersecting, forming a tree structure. We construct so-called counterflow lines (SLE[subscript 16/κ]) within the same geometry using ordered “light cones” of points accessible by angle-restricted trajectories and develop a robust theory of flow and counterflow line interaction. The theory leads to new results about SLE. For example, we prove that SLE[subscript κ](ρ) processes are almost surely continuous random curves, even when they intersect the boundary, and establish Duplantier duality for general SLE[subscript 16/κ](ρ) processes.en_US
dc.publisherSpringer-Verlagen_US
dc.relation.isversionofhttp://dx.doi.org/10.1007/s00440-016-0698-0en_US
dc.rightsCreative Commons Attributionen_US
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en_US
dc.sourceSpringer Berlin Heidelbergen_US
dc.titleImaginary geometry I: interacting SLEsen_US
dc.typeArticleen_US
dc.identifier.citationMiller, Jason, and Scott Sheffield. "Imaginary geometry I: interacting SLEs." Probability Theory and Related Fields, vol. 164, no. 3, March 2016, pp 553–705.en_US
dc.contributor.departmentMassachusetts Institute of Technology. Department of Mathematicsen_US
dc.contributor.mitauthorMiller, Jason P.
dc.contributor.mitauthorSheffield, Scott Roger
dc.relation.journalProbability Theory and Related Fieldsen_US
dc.eprint.versionFinal published versionen_US
dc.type.urihttp://purl.org/eprint/type/JournalArticleen_US
eprint.statushttp://purl.org/eprint/status/PeerRevieweden_US
dc.date.updated2016-08-18T15:27:49Z
dc.language.rfc3066en
dc.rights.holderThe Author(s)
dspace.orderedauthorsMiller, Jason; Sheffield, Scotten_US
dspace.embargo.termsNen_US
dc.identifier.orcidhttps://orcid.org/0000-0002-5951-4933
mit.licensePUBLISHER_CCen_US
mit.metadata.statusComplete


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