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dc.contributor.authorKenyon, Richarden
dc.contributor.authorMiller, Jasonen
dc.contributor.authorSheffield, Scotten
dc.contributor.authorWilson, David Bruceen
dc.date.accessioned2018-09-05T12:40:31Z
dc.date.available2018-09-05T12:40:31Z
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/279351
dc.description.abstractWe give bijections between bipolar-oriented (acyclic with unique source and sink) planar maps and certain random walks, which show that the uniformly random bipolar-oriented planar map, decorated by the "peano curve" surrounding the tree of left-most paths to the sink, converges in law with respect to the peanosphere topology to a $\sqrt{4/3}$-Liouville quantum gravity surface decorated by an independent Schramm-Loewner evolution with parameter $\kappa=12$ (i.e., SLE$_{12}$). This result is universal in the sense that it holds for bipolar-oriented triangulations, quadrangulations, $k$-angulations, and maps in which face sizes are mixed.
dc.publisherInstitute of Mathematical Statistics
dc.titleBipolar orientations on planar maps and SLE$_{12}$en
dc.typeArticle
prism.publicationNameAnnals of Probabilityen
dc.identifier.doi10.17863/CAM.26729
dcterms.dateAccepted2018-05-05en
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2018-05-05en
rioxxterms.typeJournal Article/Reviewen
pubs.funder-project-idEPSRC (EP/L018896/1)
pubs.funder-project-idEPSRC (EP/I03372X/1)
rioxxterms.freetoread.startdate2019-08-22


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