Conformal radii for conformal loop ensembles

Simple item page
dc.creatorSchramm, Oded
dc.creatorSheffield, Scott
dc.creatorWilson, David B.
dc.date2006-11-22
dc.date2009-01-19
dc.date.accessioned2026-07-07T13:05:13Z
dc.date.available2026-07-07T13:05:13Z
dc.descriptionThe conformal loop ensembles CLE(k), defined for k in [8/3, 8], are random collections of loops in a planar domain which are conjectured scaling limits of the O(n) loop models. We calculate the distribution of the conformal radii of the nested loops surrounding a deterministic point. Our results agree with predictions made by Cardy and Ziff and by Kenyon and Wilson for the O(n) model. We also compute the expectation dimension of the CLE(k) gasket, which consists of points not surrounded by any loop, to be 2-(8-k)(3k-8)/32k, which agrees with the fractal dimension given by Duplantier for the O(n) model gasket.
dc.description12 pages, v4 updates references
dc.identifierhttps://arxiv.org/abs/math/0611687
dc.identifierhttp://arxiv.org/abs/math/0611687
dc.identifierCommun.Math.Phys.288:43-53,2009
dc.identifierdoi:10.1007/s00220-009-0731-6
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227421
dc.subjectProbability
dc.subjectStatistical Mechanics
dc.subjectMathematical Physics
dc.titleConformal radii for conformal loop ensembles
dc.typetext

Files

Collections

arXiv