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dc.contributor.authorBerestycki, Nathanaelen
dc.contributor.authorLaslier, Benoiten
dc.contributor.authorRay, Gouraben
dc.date.accessioned2019-09-03T23:30:32Z
dc.date.available2019-09-03T23:30:32Z
dc.date.issued2020-01en
dc.identifier.issn0091-1798
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/296373
dc.description.abstractWe present a general result which shows that the winding of the branches in a uniform spanning tree on a planar graph converge in the limit of fine mesh size to a Gaussian free field. The result holds true assuming only convergence of simple random walk to Brownian motion and a Russo-Seymour-Welsh type crossing estimate. As an application, we prove universality of the fluctuations of the height function associated to the dimer model, in several situations. This includes the case of lozenge tilings with boundary conditions lying in a plane, and Temperleyan domains in isoradial graphs (recovering a recent result of Li). The robustness of our approach, which is a key novelty of this paper, comes from the fact that the exactly solvable nature of the model plays only a minor role in the analysis. Instead, we rely on a connection to imaginary geometry, where the limit of a uniform spanning tree is viewed as a set of flow lines associated to a Gaussian free field.
dc.publisherInstitute of Mathematical Statistics
dc.rightsAll rights reserved
dc.rights.uri
dc.subjectDimer modelen
dc.subjectimaginary geometryen
dc.subjectuniform spanning treeen
dc.subjectSLEen
dc.subjectGaussian free fielden
dc.titleDIMERS AND IMAGINARY GEOMETRYen
dc.typeArticle
prism.endingPage52
prism.issueIdentifier1en
prism.publicationDate2020en
prism.publicationNameANNALS OF PROBABILITYen
prism.startingPage1
prism.volume48en
dc.identifier.doi10.17863/CAM.43422
dcterms.dateAccepted2018-11-27en
rioxxterms.versionofrecord10.1214/18-AOP1326en
rioxxterms.versionAM
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2020-01en
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/L018896/1)
cam.orpheus.counter5*


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