Critical Exponents on Fortuin–Kasteleyn Weighted Planar Maps

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dc.contributor.authorBerestycki, Nathanaël
dc.contributor.authorLaslier, Benoît
dc.contributor.authorRay, Gourab
dc.date.accessioned2019-01-24T17:25:51Z
dc.date.available2019-01-24T17:25:51Z
dc.date.copyright2017en_US
dc.date.issued2017
dc.description.abstractIn this paper we consider random planar maps weighted by the self-dual Fortuin-Kasteleyn model with parameter q is an element of(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 annealed critical exponent associated with the length of cluster interfaces, which is shown to be 4/pi arccos (root 2-root q/2)= k'/8, where k' 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 is an element of(0,4) . Applying the KPZ formula we find that this value is consistent with the dimension of SLE curves and SLE duality.en_US
dc.description.reviewstatusRevieweden_US
dc.description.scholarlevelFacultyen_US
dc.description.sponsorshipSupported in part by EPSRC grants EP/L018896/1 and EP/I03372X/1.en_US
dc.identifier.citationBerestycki, N.; Laslier, B.; & Ray, G. (2017). Critical exponents on Fortuin- Kasteleyn weighted planar maps. Communications in Mathematical Physics, 355(2), 427-462. DOI: 10.1007/s00220-017-2933-7en_US
dc.identifier.urihttps://doi.org/10.1007/s00220-017-2933-7
dc.identifier.urihttp://hdl.handle.net/1828/10531
dc.language.isoenen_US
dc.publisherCommunications in Mathematical Physicsen_US
dc.subject.departmentDepartment of Mathematics and Statistics
dc.titleCritical Exponents on Fortuin–Kasteleyn Weighted Planar Mapsen_US
dc.typeArticleen_US

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