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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)


Boundary behavior of SLE

Author: Nam-Gyu Kang
Journal: J. Amer. Math. Soc. 20 (2007), 185-210
MSC (2000): Primary 30C45, 60K35; Secondary 28A80, 60J65
Published electronically: August 28, 2006
MathSciNet review: 2257400
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Abstract: We show that the normalized (pre-)Schwarzian derivative of SLE, after we subtract a negligible term, is a complex BMO martingale. Its BMO norm gives strong evidence for Duplantier's duality conjecture. We also show that it has correlations that decay exponentially in the hyperbolic distance.

We reexamine S. Rohde and O. Schramm's derivative expectation to derive the conjectured sharp estimate for the Hölder exponent unless the parameter of SLE is 4.

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Additional Information

Nam-Gyu Kang
Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

PII: S 0894-0347(06)00547-9
Keywords: SLE, Schwarzian derivatives, H\"{o}lder continuity, Duplantier's duality conjecture
Received by editor(s): January 31, 2005
Published electronically: August 28, 2006
Additional Notes: This research was partially conducted during the period when the author was employed by the Clay Mathematical Institute as a Liftoff Fellow. The author is partially supported by NSF grant DMS 05-05751.
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.