English

On the Continuity of SLE(\kappa) in \kappa

Probability 2012-06-12 v1

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})=2.143... 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.

Keywords

Cite

@article{arxiv.1206.1956,
  title  = {On the Continuity of SLE(\kappa) in \kappa},
  author = {Fredrik Johansson Viklund and Steffen Rohde and Carto Wong},
  journal= {arXiv preprint arXiv:1206.1956},
  year   = {2012}
}

Comments

17 pages, 1 figure