论文标题
多重点弦弦$ \ mathrm {sle}_κ（\uneslineρ）$的时间逆转
Time-reversal of multiple-force-point chordal $\mathrm{SLE}_κ(\underlineρ)$
论文作者
论文摘要
Chordal SLE $_κ（\ lundlineC）$是弦SLE曲线的自然变体。它是从0到$ \ infty $的上半飞机上随机非交叉曲线的家族，其法律受$ \ Mathbb r $ $ $ $ \ Mathbb r $的额外力点的影响。当有力点远离原点时，SLE $_κ（\ lundlineC）$的定律并不是普通的和弦SLE $_κ$。 Zhan（2019）对SLE $_κ（\useplineρ）$的时间逆转定律进行了明确的描述。在本文中，我们证明了他的猜想。特别是，根据Zhan的结果，使用Miller和Sheffield（2013）开发的虚构几何形状的技术，我们表明，当$κ\ in（0,8）$（0,8）$时，非实时填充$ \ mathrm {slerm {slerm {sle}_κ（\ underlineC）$的时间逆转的定律是绝对的。 $ \ mathrm {sle}_κ（\下划线{\hatρ}）$对于某些$ \ usewissline {\hatρ} $由$ \ usewiseplineρ$确定，radon-nikodym衍生物是共同衍生物的产物。
Chordal SLE$_κ(\underlineρ)$ is a natural variant of chordal SLE curve. It is a family of random non-crossing curves on the upper half plane from 0 to $\infty$, whose law is influenced by additional force points on $\mathbb R$. When there are force points away from the origin, the law of SLE$_κ(\underlineρ)$ is not reversible as the ordinary chordal SLE$_κ$. Zhan (2019) give an explicit description of the law of the time reversal of SLE$_κ(\underlineρ)$ when all force points lies on the same sides of the origin, and conjectured that a similar result holds in general. In this paper we prove his conjecture. In particular, based on Zhan's result, using the techniques from the Imaginary Geometry developed by Miller and Sheffield (2013), we show that when $κ\in(0,8)$, the law of the time reversal of non-boundary filling $\mathrm{SLE}_κ(\underlineρ)$ process is absolutely continuous with respect to $\mathrm{SLE}_κ(\underline{\hatρ})$ for some $\underline{\hatρ}$ determined by $\underlineρ$, with the Radon-Nikodym derivative being a product of conformal derivatives.
