Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces
dc.contributor.author | Miller, Jason | |
dc.contributor.author | Sheffield, Scott | |
dc.contributor.author | Werner, Wendelin | |
dc.date.accessioned | 2021-11-22T14:42:52Z | |
dc.date.available | 2021-11-22T14:42:52Z | |
dc.date.issued | 2021-06-26 | |
dc.date.submitted | 2020-07-02 | |
dc.identifier.issn | 0178-8051 | |
dc.identifier.other | s00440-021-01070-4 | |
dc.identifier.other | 1070 | |
dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/330863 | |
dc.description.abstract | Abstract: 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.language | en | |
dc.publisher | Springer Berlin Heidelberg | |
dc.subject | Article | |
dc.subject | Conformal loop ensembles | |
dc.subject | Liouville quantum gravity | |
dc.subject | Percolation | |
dc.subject | Gaussian free field | |
dc.subject | Schramm–Loewner evolutions | |
dc.subject | Growth–fragmentation trees | |
dc.subject | 60J67 | |
dc.subject | 60K35 | |
dc.subject | 82B41 | |
dc.subject | 82B27 | |
dc.subject | 60G52 | |
dc.subject | 60G60 | |
dc.subject | 60J80 | |
dc.title | Non-simple conformal loop ensembles on Liouville quantum gravity and the law of CLE percolation interfaces | |
dc.type | Article | |
dc.date.updated | 2021-11-22T14:42:51Z | |
prism.endingPage | 710 | |
prism.issueIdentifier | 1-3 | |
prism.publicationName | Probability Theory and Related Fields | |
prism.startingPage | 669 | |
prism.volume | 181 | |
dc.identifier.doi | 10.17863/CAM.78306 | |
dcterms.dateAccepted | 2021-06-02 | |
rioxxterms.versionofrecord | 10.1007/s00440-021-01070-4 | |
rioxxterms.version | VoR | |
rioxxterms.licenseref.uri | http://creativecommons.org/licenses/by/4.0/ | |
dc.identifier.eissn | 1432-2064 | |
pubs.funder-project-id | European Research Council (804166) | |
pubs.funder-project-id | Directorate for Mathematical and Physical Sciences (DMS-1712862) | |
pubs.funder-project-id | SNF (175505) |
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