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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Hölder regularity of the SLE trace


Author: Joan R. Lind
Journal: Trans. Amer. Math. Soc. 360 (2008), 3557-3578
MSC (2000): Primary 60D05, 30C35, 60G17
Published electronically: January 9, 2008
MathSciNet review: 2386236
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Abstract: S. Rohde and O. Schramm have recently shown that the SLE trace is Hölder continuous (2005). However, their results are not optimal for all values of $ \kappa$ and only yield a Hölder exponent near $ \frac{1}{2}$ for $ \kappa$ near 0. In this paper, we give improved lower bounds on the optimal Hölder exponent for two natural parametrizations of the SLE trace. Our estimates give a Hölder exponent near 1 for $ \kappa$ near 0, as expected. The work of I. Binder and B. Duplantier (2002) suggests that our results are optimal for the two parametrizations considered.


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Additional Information

Joan R. Lind
Affiliation: Department of Mathematics, Belmont University, 1900 Belmont Boulevard, Nashville, Tennessee 37212

DOI: http://dx.doi.org/10.1090/S0002-9947-08-04327-4
PII: S 0002-9947(08)04327-4
Received by editor(s): February 24, 2005
Received by editor(s) in revised form: April 22, 2006
Published electronically: January 9, 2008
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.