Regularity of SLE in (t,κ) and refined GRR estimates

dc.contributor.authorFriz, Peter K.
dc.contributor.authorTran, Huy
dc.contributor.authorYuan, Yizheng
dc.date.accessioned2021-07-07T07:21:40Z
dc.date.available2021-07-07T07:21:40Z
dc.date.issued2021-05-06
dc.description.abstractSchramm–Loewner evolution (SLEκ) is classically studied via Loewner evolution with half-plane capacity parametrization, driven by √k times Brownian motion. This yields a (half-plane) valued random field γ=γ(t,κ;ω). (Hölder) regularity of in γ(⋅,κ;ω), a.k.a. SLE trace, has been considered by many authors, starting with Rohde and Schramm (Ann Math (2) 161(2):883–924, 2005). Subsequently, Johansson Viklund et al. (Probab Theory Relat Fields 159(3–4):413–433, 2014) showed a.s. Hölder continuity of this random field for κ<8(2−√3). In this paper, we improve their result to joint Hölder continuity up to κ<8/3. Moreover, we show that the SLEκ trace γ(⋅,κ) (as a continuous path) is stochastically continuous in κ at all κ≠8. Our proofs rely on a novel variation of the Garsia–Rodemich–Rumsey inequality, which is of independent interest.en
dc.description.sponsorshipTU Berlin, Open-Access-Mittel – 2021en
dc.identifier.eissn1432-2064
dc.identifier.issn0178-8051
dc.identifier.urihttps://depositonce.tu-berlin.de/handle/11303/13367
dc.identifier.urihttp://dx.doi.org/10.14279/depositonce-12156
dc.language.isoenen
dc.relation.ispartof10.14279/depositonce-15455en
dc.rights.urihttps://creativecommons.org/licenses/by/4.0/en
dc.subject.ddc510 Mathematikde
dc.subject.otherSchramm–Loewner evolutionen
dc.subject.otherBrownian motionen
dc.subject.otherGarsia–Rodemich–Rumsey inequalityen
dc.titleRegularity of SLE in (t,κ) and refined GRR estimatesen
dc.typeArticleen
dc.type.versionpublishedVersionen
dcterms.bibliographicCitation.doi10.1007/s00440-021-01058-0en
dcterms.bibliographicCitation.journaltitleProbability Theory and Related Fieldsen
dcterms.bibliographicCitation.originalpublishernameSpringer Natureen
dcterms.bibliographicCitation.originalpublisherplaceHeidelbergen
dcterms.bibliographicCitation.pageend112en
dcterms.bibliographicCitation.pagestart71en
dcterms.bibliographicCitation.volume180en
tub.accessrights.dnbfreeen
tub.affiliationFak. 2 Mathematik und Naturwissenschaften>Inst. Mathematik>AG Stochastik und Finanzmathematikde
tub.affiliation.facultyFak. 2 Mathematik und Naturwissenschaftende
tub.affiliation.groupAG Stochastik und Finanzmathematikde
tub.affiliation.instituteInst. Mathematikde
tub.publisher.universityorinstitutionTechnische Universität Berlinen
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