Continuity of the SLE trace in simply connected domains

Christophe Garban; Steffen Rohde; Oded Schramm

Continuity of the SLE trace in simply connected domains

Probability 2008-11-19 v2 Mathematical Physics Complex Variables math.MP

Authors: Christophe Garban , Steffen Rohde , Oded Schramm

Abstract

We prove that the $SLE_\kappa$ trace in any simply connected domain $G$ is continuous (except possibly near its endpoints) if $\kappa<8$ . We also prove an SLE analog of Makarov's Theorem about the support of harmonic measure.

Keywords

SLE trace continuity simply connected domain harmonic measure Makarov's theorem

Cite

@article{arxiv.0810.4327,
  title  = {Continuity of the SLE trace in simply connected domains},
  author = {Christophe Garban and Steffen Rohde and Oded Schramm},
  journal= {arXiv preprint arXiv:0810.4327},
  year   = {2008}
}

Comments

15 pages, 2 figures. Statement of theorem 1.2 corrected

Continuity of the SLE trace in simply connected domains

Abstract

Keywords

Cite

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