English

A support theorem for SLE curves

Probability 2020-02-07 v3 Complex Variables

Abstract

For all κ>0\kappa > 0, we show that the support of SLEκ_\kappa curves is the closure in the sup-norm of the set of Loewner curves driven by nice (e.g. smooth) functions. It follows that the support is the closure of the set of simple curves starting at 00.

Keywords

Cite

@article{arxiv.1810.10843,
  title  = {A support theorem for SLE curves},
  author = {Huy Tran and Yizheng Yuan},
  journal= {arXiv preprint arXiv:1810.10843},
  year   = {2020}
}
R2 v1 2026-06-23T04:52:28.575Z