Bipolar orientations on planar maps and SLE 12
| cam.issuedOnline | 2019-05-01 | |
| dc.contributor.author | Kenyon, R | |
| dc.contributor.author | Miller, J | |
| dc.contributor.author | Sheffield, S | |
| dc.contributor.author | Wilson, DB | |
| dc.date.accessioned | 2018-09-05T12:40:31Z | |
| dc.date.available | 2018-09-05T12:40:31Z | |
| dc.date.issued | 2019 | |
| dc.description.abstract | We 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.identifier.doi | 10.17863/CAM.26729 | |
| dc.identifier.issn | 0091-1798 | |
| dc.identifier.uri | https://www.repository.cam.ac.uk/handle/1810/279351 | |
| dc.publisher | Institute of Mathematical Statistics | |
| dc.publisher.url | http://dx.doi.org/10.1214/18-aop1282 | |
| dc.subject | Bipolar oriention | |
| dc.subject | random planar map | |
| dc.subject | Schramm-Loewner evolution | |
| dc.subject | Liouville quantum gravity | |
| dc.subject | continuum random tree | |
| dc.title | Bipolar orientations on planar maps and SLE <inf>12</inf> | |
| dc.type | Article | |
| dcterms.dateAccepted | 2018-05-05 | |
| prism.publicationName | Annals of Probability | |
| pubs.funder-project-id | Engineering and Physical Sciences Research Council (EP/I03372X/1) | |
| pubs.funder-project-id | Engineering and Physical Sciences Research Council (EP/L018896/1) | |
| rioxxterms.licenseref.startdate | 2018-05-05 | |
| rioxxterms.licenseref.uri | http://www.rioxx.net/licenses/all-rights-reserved | |
| rioxxterms.type | Journal Article/Review | |
| rioxxterms.version | AM | |
| rioxxterms.versionofrecord | 10.1214/18-AOP1282 |
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