Regularity of SLE in (t,κ) and refined GRR estimates
dc.contributor.author | Friz, Peter K. | |
dc.contributor.author | Tran, Huy | |
dc.contributor.author | Yuan, Yizheng | |
dc.date.accessioned | 2021-07-07T07:21:40Z | |
dc.date.available | 2021-07-07T07:21:40Z | |
dc.date.issued | 2021-05-06 | |
dc.description.abstract | Schramm–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.sponsorship | TU Berlin, Open-Access-Mittel – 2021 | en |
dc.identifier.eissn | 1432-2064 | |
dc.identifier.issn | 0178-8051 | |
dc.identifier.uri | https://depositonce.tu-berlin.de/handle/11303/13367 | |
dc.identifier.uri | http://dx.doi.org/10.14279/depositonce-12156 | |
dc.language.iso | en | en |
dc.relation.ispartof | 10.14279/depositonce-15455 | en |
dc.rights.uri | https://creativecommons.org/licenses/by/4.0/ | en |
dc.subject.ddc | 510 Mathematik | de |
dc.subject.other | Schramm–Loewner evolution | en |
dc.subject.other | Brownian motion | en |
dc.subject.other | Garsia–Rodemich–Rumsey inequality | en |
dc.title | Regularity of SLE in (t,κ) and refined GRR estimates | en |
dc.type | Article | en |
dc.type.version | publishedVersion | en |
dcterms.bibliographicCitation.doi | 10.1007/s00440-021-01058-0 | en |
dcterms.bibliographicCitation.journaltitle | Probability Theory and Related Fields | en |
dcterms.bibliographicCitation.originalpublishername | Springer Nature | en |
dcterms.bibliographicCitation.originalpublisherplace | Heidelberg | en |
dcterms.bibliographicCitation.pageend | 112 | en |
dcterms.bibliographicCitation.pagestart | 71 | en |
dcterms.bibliographicCitation.volume | 180 | en |
tub.accessrights.dnb | free | en |
tub.affiliation | Fak. 2 Mathematik und Naturwissenschaften::Inst. Mathematik::AG Stochastik und Finanzmathematik | de |
tub.affiliation.faculty | Fak. 2 Mathematik und Naturwissenschaften | de |
tub.affiliation.group | AG Stochastik und Finanzmathematik | de |
tub.affiliation.institute | Inst. Mathematik | de |
tub.publisher.universityorinstitution | Technische Universität Berlin | en |