Mathematics – Probability
Scientific paper
2007-12-03
Mathematics
Probability
In this third version, the referee's suggestions are taken into consideration. More details are added. Some typos are correcte
Scientific paper
10.1007/s00222-008-0132-z
We derive some geometric properties of chordal SLE$(\kappa;\vec{\rho})$ processes. Using these results and the method of coupling two SLE processes, we prove that the outer boundary of the final hull of a chordal SLE$(\kappa;\vec{\rho})$ process has the same distribution as the image of a chordal SLE$(\kappa';\vec{\rho'})$ trace, where $\kappa>4$, $\kappa'=16/\kappa$, and the forces $\vec{\rho}$ and $\vec{\rho'}$ are suitably chosen. We find that for $\kappa\ge 8$, 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 $x$. Then we obtain a new proof of the fact that chordal SLE$(\kappa)$ trace is not reversible for $\kappa>8$. We also prove that the reversal of SLE$(4;\vec{\rho})$ trace has the same distribution as the time-change of some SLE$(4;\vec{\rho'})$ trace for certain values of $\vec{\rho}$ and $\vec{\rho'}$.
No associations
LandOfFree
Duality of Chordal SLE does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Duality of Chordal SLE, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Duality of Chordal SLE will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-51313