dc.contributor.author Berestycki, Nathanael en dc.contributor.author Laslier, Benoit en dc.contributor.author Ray, Gourab en dc.date.accessioned 2017-11-09T17:05:41Z dc.date.available 2017-11-09T17:05:41Z dc.date.issued 2017-10-01 en dc.identifier.issn 0010-3616 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/268296 dc.description.abstract In 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.sponsorship Nathanaël 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.publisher Springer dc.rights Attribution 4.0 International en dc.rights Attribution 4.0 International en dc.rights.uri http://creativecommons.org/licenses/by/4.0/ en dc.rights.uri http://creativecommons.org/licenses/by/4.0/ en dc.title Critical Exponents on Fortuin-Kasteleyn Weighted Planar Maps en dc.type Article prism.endingPage 462 prism.issueIdentifier 2 en prism.publicationDate 2017 en prism.publicationName COMMUNICATIONS IN MATHEMATICAL PHYSICS en prism.startingPage 427 prism.volume 355 en dc.identifier.doi 10.17863/CAM.10803 dcterms.dateAccepted 2017-05-12 en rioxxterms.versionofrecord 10.1007/s00220-017-2933-7 en rioxxterms.version AM * rioxxterms.licenseref.uri http://creativecommons.org/licenses/by/4.0/ en rioxxterms.licenseref.startdate 2017-10-01 en dc.identifier.eissn 1432-0916 rioxxterms.type Journal Article/Review en pubs.funder-project-id EPSRC (EP/I03372X/1) pubs.funder-project-id EPSRC (EP/L018896/1) cam.issuedOnline 2017-07-22 en rioxxterms.freetoread.startdate 2018-07-22
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