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Duality of chordal SLE. II. (English) Zbl 1200.60071
Summary: 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 \(x\in \mathbb R \setminus \{0\}\) 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 \(\kappa \geq 8\), 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, a chordal or strip SLE\((\kappa ; \vec{\rho })\) trace a.s. ends at a single point.
For part I, cf. Invent. Math. 174, No. 2, 309–353 (2008; Zbl 1158.60047).

MSC:
60J67 Stochastic (Schramm-)Loewner evolution (SLE)
30C20 Conformal mappings of special domains
60H05 Stochastic integrals
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