Show simple item record

dc.contributor.authorMiller, Jason
dc.contributor.authorSheffield, Scott
dc.contributor.authorWerner, Wendelin
dc.date.accessioned2021-11-22T14:42:52Z
dc.date.available2021-11-22T14:42:52Z
dc.date.issued2021-06-26
dc.date.submitted2020-07-02
dc.identifier.issn0178-8051
dc.identifier.others00440-021-01070-4
dc.identifier.other1070
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/330863
dc.description.abstractAbstract: We study the structure of the Liouville quantum gravity (LQG) surfaces that are cut out as one explores a conformal loop-ensemble CLEκ′ for κ′ in (4, 8) that is drawn on an independent γ-LQG surface for γ2=16/κ′. The results are similar in flavor to the ones from our companion paper dealing with CLEκ for κ in (8/3, 4), where the loops of the CLE are disjoint and simple. In particular, we encode the combined structure of the LQG surface and the CLEκ′ in terms of stable growth-fragmentation trees or their variants, which also appear in the asymptotic study of peeling processes on decorated planar maps. This has consequences for questions that do a priori not involve LQG surfaces: In our paper entitled “CLE Percolations” described the law of interfaces obtained when coloring the loops of a CLEκ′ independently into two colors with respective probabilities p and 1-p. This description was complete up to one missing parameter ρ. The results of the present paper about CLE on LQG allow us to determine its value in terms of p and κ′. It shows in particular that CLEκ′ and CLE16/κ′ are related via a continuum analog of the Edwards-Sokal coupling between FKq percolation and the q-state Potts model (which makes sense even for non-integer q between 1 and 4) if and only if q=4cos2(4π/κ′). This provides further evidence for the long-standing belief that CLEκ′ and CLE16/κ′ represent the scaling limits of FKq percolation and the q-Potts model when q and κ′ are related in this way. Another consequence of the formula for ρ(p, κ′) is the value of half-plane arm exponents for such divide-and-color models (a.k.a. fuzzy Potts models) that turn out to take a somewhat different form than the usual critical exponents for two-dimensional models.
dc.languageen
dc.publisherSpringer Berlin Heidelberg
dc.subjectArticle
dc.subjectConformal loop ensembles
dc.subjectLiouville quantum gravity
dc.subjectPercolation
dc.subjectGaussian free field
dc.subjectSchramm–Loewner evolutions
dc.subjectGrowth–fragmentation trees
dc.subject60J67
dc.subject60K35
dc.subject82B41
dc.subject82B27
dc.subject60G52
dc.subject60G60
dc.subject60J80
dc.titleNon-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces
dc.typeArticle
dc.date.updated2021-11-22T14:42:51Z
prism.endingPage710
prism.issueIdentifier1-3
prism.publicationNameProbability Theory and Related Fields
prism.startingPage669
prism.volume181
dc.identifier.doi10.17863/CAM.78306
dcterms.dateAccepted2021-06-02
rioxxterms.versionofrecord10.1007/s00440-021-01070-4
rioxxterms.versionVoR
rioxxterms.licenseref.urihttp://creativecommons.org/licenses/by/4.0/
dc.identifier.eissn1432-2064
pubs.funder-project-idEuropean Research Council (804166)
pubs.funder-project-idDirectorate for Mathematical and Physical Sciences (DMS-1712862)
pubs.funder-project-idSNF (175505)


Files in this item

Thumbnail
Thumbnail

This item appears in the following Collection(s)

Show simple item record