TITLE

On the continuity of $$\text{ SLE }_{\kappa }$$ in $$\kappa $$

AUTHOR(S)
Johansson Viklund, Fredrik; Rohde, Steffen; Wong, Carto
PUB. DATE
August 2014
SOURCE
Probability Theory & Related Fields;Aug2014, Vol. 159 Issue 3/4, p413
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
We prove that for almost every Brownian motion sample, the corresponding SLE $$_\kappa $$ curves parameterized by capacity exist and change continuously in the supremum norm when $$\kappa $$ varies in the interval $$[0,\kappa _0)$$ , where $$\kappa _0=8(2-\sqrt{3})\approx 2.1$$ . We estimate the $$\kappa $$ -dependent modulus of continuity of the curves and also give an estimate on the modulus of continuity for the supremum norm change with $$\kappa $$ .
ACCESSION #
96985784

 

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