论文标题
SLE相过渡的新方法
A new approach to SLE phase transition
论文作者
论文摘要
众所周知，$SLE_κ$曲线在$κ= 4 $时表现出相变。对于$κ\ le 4 $，它们是一个简单的曲线，概率是一条，对于$κ> 4 $，它们不是。标准证明是基于对维度$ d = 1+4/κ$的贝塞尔SDE的分析。我们提出了一种不同的方法，该方法基于对Bessel SDE的分析，其$ d = 1-4/κ$。这不仅给出了新的视角，而且还允许以$κ> 4 $的形式描述SLE“气泡”的形成。
It is well know that $SLE_κ$ curves exhibit a phase transition at $κ=4$. For $κ\le 4$ they are simple curves with probability one, for $κ>4$ they are not. The standard proof is based on the analysis of the Bessel SDE of dimension $d=1+4/κ$. We propose a different approach which is based on the analysis of the Bessel SDE with $d=1-4/κ$. This not only gives a new perspective, but also allows to describe the formation of the SLE `bubbles' for $κ>4$.
