Boundary behavior of SLE
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- by Nam-Gyu Kang;
- J. Amer. Math. Soc. 20 (2007), 185-210
- DOI: https://doi.org/10.1090/S0894-0347-06-00547-9
- Published electronically: August 28, 2006
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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.References
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Bibliographic Information
- Nam-Gyu Kang
- Affiliation: Department of Mathematics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139
- MR Author ID: 687219
- ORCID: 0000-0003-4545-6899
- Email: kang@math.mit.edu
- 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.
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: J. Amer. Math. Soc. 20 (2007), 185-210
- MSC (2000): Primary 30C45, 60K35; Secondary 28A80, 60J65
- DOI: https://doi.org/10.1090/S0894-0347-06-00547-9
- MathSciNet review: 2257400