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dc.contributor.authorBerestycki, Nathanaelen
dc.contributor.authorLaslier, Benoiten
dc.contributor.authorRay, Gouraben
dc.date.accessioned2017-11-09T17:05:41Z
dc.date.available2017-11-09T17:05:41Z
dc.date.issued2017-10-01en
dc.identifier.issn0010-3616
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/268296
dc.description.abstractIn this paper we consider random planar maps weighted by the self-dual Fortuin--Kasteleyn model with parameter $q \in (0,4)$. Using a bijection due to Sheffield and a connection to planar Brownian motion in a cone we obtain rigorously the value of the critical exponent associated with the length of cluster interfaces, which is shown to be $$ \frac{4}{\pi} \arccos \left( \frac{\sqrt{2 - \sqrt{q}}}{2} \right)=\frac{\kappa'}{8}. $$ where $\kappa' $ is the SLE parameter associated with this model. We also derive the exponent corresponding to the area enclosed by a loop which is shown to be 1 for all values of $q \in (0,4)$. Applying the KPZ formula we find that this value is consistent with the dimension of SLE curves and SLE duality. Communicated by H.-T. Yau
dc.description.sponsorshipNathanaël Berestycki: Supported in part by EPSRC grants EP/L018896/1 and EP/I03372X/1. Benoît Laslier: Supported in part by EPSRC grant EP/I03372X/1. Gourab Ray: Supported in part by EPSRC grant EP/I03372X/1.
dc.publisherSpringer
dc.rightsAttribution 4.0 Internationalen
dc.rightsAttribution 4.0 Internationalen
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/en
dc.titleCritical Exponents on Fortuin-Kasteleyn Weighted Planar Mapsen
dc.typeArticle
prism.endingPage462
prism.issueIdentifier2en
prism.publicationDate2017en
prism.publicationNameCOMMUNICATIONS IN MATHEMATICAL PHYSICSen
prism.startingPage427
prism.volume355en
dc.identifier.doi10.17863/CAM.10803
dcterms.dateAccepted2017-05-12en
rioxxterms.versionofrecord10.1007/s00220-017-2933-7en
rioxxterms.versionAM*
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/en
rioxxterms.licenseref.startdate2017-10-01en
dc.identifier.eissn1432-0916
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/I03372X/1)
pubs.funder-project-idEPSRC (EP/L018896/1)
cam.issuedOnline2017-07-22en
rioxxterms.freetoread.startdate2018-07-22


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Attribution 4.0 International
Except where otherwise noted, this item's licence is described as Attribution 4.0 International