Speaker : Nam-Gyu Kang (California Institute of Technology)
Date : 2008. 9. 4(THU) 17:20-18:20
Place : E6-1 #1409
Title: Boundary behavior of SLE
Abstract: I reexamine S. Rohde and O. Schramm's derivative expectation to obtain the conjectured sharp estimate for the Hölder exponent unless the parameter of SLE is 4. I also derive the conjectured sharp upper bound in the law of the iterated logarithm for SLE. This leads us to compare the harmonic measure of the SLE boundary to the Hausdorff measure associated with a logarithmicoexponential function. I show that the normalized (pre-)Schwarzian derivative of SLE, after we subtract a negligible term, is a complex martingale. I also show that it has correlations that decay exponentially in the hyperbolic distance.