Duality of chordal SLE
Duality of chordal SLE
复制标题
弦索 SLE 的二元性
DOI：
10.1007/s00222-008-0132-z
复制
发表时间：
2007
影响因子：
3.1
通讯作者：
Dapeng Zhan
中科院分区：
文献类型：
--
作者：
Dapeng Zhan
We derive some geometric properties of chordal SLE(κ;$\vec{\rho}$) 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(κ;$\vec{\rho}$) process has the same distribution as the image of a chordal SLE(κ’;$\vec{\rho}$’) trace, where κ>4, κ’=16/κ, and the forces $\vec{\rho}$ and $\vec{\rho}$’ are suitably chosen. We find that for κ≥8, the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed $x\in\mathbb{R}\setminus\{0\}$ is the image of some SLE(16/κ;$\vec{\rho}$) trace started from x. Then we obtain a new proof of the fact that chordal SLE(κ) trace is not reversible for κ>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 $\vec{\rho}$’.
We derive some geometric properties of chordal SLE(κ;$\vec{\rho}$) 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(κ;$\vec{\rho}$) process has the same distribution as the image of a chordal SLE(κ’;$\vec{\rho}$’) trace, where κ>4, κ’=16/κ, and the forces $\vec{\rho}$ and $\vec{\rho}$’ are suitably chosen. We find that for κ≥8, the boundary of a standard chordal SLE(κ) hull stopped on swallowing a fixed $x\in\mathbb{R}\setminus\{0\}$ is the image of some SLE(16/κ;$\vec{\rho}$) trace started from x. Then we obtain a new proof of the fact that chordal SLE(κ) trace is not reversible for κ>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 $\vec{\rho}$’.