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ON THE REGULARITY OF SLE TRACE

Part of: Markov processes

Published online by Cambridge University Press:  24 August 2017

PETER K. FRIZ  and
HUY TRAN
PETER K. FRIZ
Affiliation:
Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, D-10623, Berlin; friz@math.tu-berlin.de
HUY TRAN
Affiliation:
University of California, Los Angeles, Department of Mathematics, Los Angeles, CA 90095-1555, USA; tvhuy@math.ucla.edu

Abstract

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We revisit regularity of SLE trace, for all $\unicode[STIX]{x1D705}\neq 8$, and establish Besov regularity under the usual half-space capacity parametrization. With an embedding theorem of Garsia–Rodemich–Rumsey type, we obtain finite moments (and hence almost surely) optimal variation regularity with index $\min (1+\unicode[STIX]{x1D705}/8,2)$, improving on previous works of Werness, and also (optimal) Hölder regularity à la Johansson Viklund and Lawler.

MSC classification

Primary: 60J67: Stochastic (Schramm-)Loewner evolution (SLE)
Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 5 , 2017 , e19
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2017

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