Duality of Chordal SLE, II

Abstract

We improve the geometric properties of SLE$(\kappa ;\vec{\rho })$ processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for $\kappa \in (4,8)$, the boundary of a standard chordal SLE$(\kappa )$ hull stopped on swallowing a fixed $x\in\R\sem\{0\}$ is the image of some SLE$(16/\kappa ;\vec{\rho })$ trace started from a random point. Using this fact together with a similar proposition in the case that $\kappa \ge 8$, we obtain a description of the boundary of a standard chordal SLE$(\kappa )$ hull for $\kappa >4$, at a finite stopping time. Finally, we prove that for $\kappa >4$, in many cases, the limit of a chordal or strip SLE$(\kappa ;\vec{\rho })$ trace exists.

30 pages; some changes have been made to Introduction and References

References in corpus (1)

• Duality of Schramm-Loewner Evolutions