Duality of chordal SLE, II

作者：Zhan Dapeng^*

来源：Annales de l Institut Henri Poincare-Probabilites et Statistiques, 2010, 46(3): 740-759.

DOI：10.1214/09-AIHP340

• SLE
• Duality
• Coupling technique

We improve the geometric properties of SLE(kappa;(rho) over right arrow) processes derived in an earlier paper, which are then used to obtain more results about the duality of SLE. We find that for kappa is an element of (4, 8), the boundary of a standard chordal SLE(kappa) hull stopped on swallowing a fixed x is an element of R \ {0} is the image of some SLE(16/kappa; (rho) over right arrow) trace started from a random point. Using this fact together with a similar proposition in the case that K >= 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;(rho) over right arrow) trace a.s. ends at a single point.

• 出版日期2010-8