arXiv subjects
Publications and source records attributed to Stephen Yearwood.
We give a new proof of the reversibility of the Schramm Loewner evolution for $κ\leq 4$. The main ideas used in the proof are similar to those used in the original proof of this result, given by Zhan.
We study the topology of $SLE$ curves for $κ> 4$. More precisely, we show that, a.s., there is no homeomorphism $Φ: \overline{\mathbb{H}} \rightarrow \overline{\mathbb{H}}$, taking the range of one independent $SLE$ curve to another for $κ\in (4,8)$. Furthermore, we extend the result to $κ\geq 8$ by showing that there is no homeomorphism taking one $SLE$ curve to another, when viewed as curves modulo parametrization.