Coupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines

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cam.issuedOnline2018-06-01
dc.contributor.authorQian, W
dc.contributor.authorWerner, Wendelin
dc.contributor.orcidQian, Wei [0000-0002-4779-4042]
dc.date.accessioned2018-08-13T09:21:46Z
dc.date.available2018-08-13T09:21:46Z
dc.date.issued2018-07-01
dc.description.abstractWe point out a new simple way to couple the Gaussian free field (GFF) with free boundary conditions in a two-dimensional domain with the GFF with zero boundary conditions in the same domain: Starting from the latter, one just has to sample at random all the signs of the height gaps on its boundary-touching zero level lines (these signs are alternating for the zero-boundary GFF) in order to obtain a free boundary GFF. Constructions and couplings of the free boundary GFF and its level lines via soups of reflected Brownian loops and their clusters are also discussed. Such considerations show for instance that in a domain with an axis of symmetry, if one looks at the overlay of a single usual Conformal Loop Ensemble CLE3 with its own symmetric image, one obtains the CLE4-type collection of level lines of a GFF with mixed zero/free boundary conditions in the half-domain.
dc.description.sponsorshipWe acknowledge support of the Grant No. 155922 (WQ, WW) and an Early Postdoc.Mobility Grant (WQ) of the SNF. The authors are/were part of NCCR SwissMAP
dc.identifier.doi10.17863/CAM.26161
dc.identifier.issn1432-0916
dc.identifier.urihttps://www.repository.cam.ac.uk/handle/1810/278794
dc.languageeng
dc.publisherSpringer Nature
dc.rightsAttribution 4.0 International
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/
dc.titleCoupling the Gaussian Free Fields with Free and with Zero Boundary Conditions via Common Level Lines
dc.typeArticle
dcterms.dateAccepted2018-03-02
prism.endingPage80
prism.issueIdentifier1
prism.publicationDate2018
prism.publicationNameCommunications in Mathematical Physics
prism.startingPage53
prism.volume361
rioxxterms.licenseref.startdate2018-07-01
rioxxterms.licenseref.urihttp://www.rioxx.net/licenses/all-rights-reserved
rioxxterms.typeJournal Article/Review
rioxxterms.versionVoR
rioxxterms.versionofrecord10.1007/s00220-018-3159-z
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