Boundary behavior of SLE

Kang, Nam-Gyu

doi:10.1090/S0894-0347-06-00547-9

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.

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