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dc.contributor.authorGwynne, Ewainen
dc.contributor.authorKassel, Adrienen
dc.contributor.authorMiller, Jasonen
dc.contributor.authorWilson, David Ben
dc.date.accessioned2018-03-07T17:55:00Z
dc.date.available2018-03-07T17:55:00Z
dc.date.issued2018-03en
dc.identifier.issn0010-3616
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/273804
dc.description.abstractWe consider the Peano curve separating a spanning tree from its dual spanning tree on an embedded planar graph, where the tree and dual tree are weighted by $y$ to the number of active edges, and "active" is in the sense of the Tutte polynomial. When the graph is a portion of the square grid approximating a simply connected domain, it is known ($y=1$ and $y=1+\sqrt{2}$) or believed ($1<y<3$) that the Peano curve converges to a space-filling SLE$_{\kappa}$ loop, where $y=1-2\cos(4\pi/\kappa)$, corresponding to $4<\kappa\leq 8$. We argue that the same should hold for $0\le y<1$, which corresponds to $8<\kappa\leq 12$.
dc.languageenen
dc.publisherSpringer Nature
dc.titleActive Spanning Trees with Bending Energy on Planar Maps and SLE-Decorated Liouville Quantum Gravity for $${\kappa > 8}$$en
dc.typeArticle
prism.endingPage1115
prism.issueIdentifier3en
prism.publicationDate2018en
prism.publicationNameCommunications in Mathematical Physicsen
prism.startingPage1065
prism.volume358en
dc.identifier.doi10.17863/CAM.20873
dcterms.dateAccepted2017-12-22en
rioxxterms.versionofrecord10.1007/s00220-018-3104-1en
rioxxterms.versionAM*
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserveden
rioxxterms.licenseref.startdate2018-03en
dc.identifier.eissn1432-0916
rioxxterms.typeJournal Article/Reviewen
cam.issuedOnline2018-02-14en
rioxxterms.freetoread.startdate2019-02-14


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