论文标题
在形式的共同体上的共同协变量测量的存在和独特性
Existence and uniqueness of the conformally covariant volume measure on conformal loop ensembles
论文作者
论文摘要
我们证明了在保形环集合的地毯/垫圈上的规范共变量体积测量的存在和独特性（CLE $_κ$，$κ\ in（8/3,8）$），这尊重Markov的CLE属性。该构建的起点是在先前由谢菲尔德和沃纳（Sheffield and Werner）的第一作者构建的liouville量子重力（LQG）的背景下，在CLE上存在规范措施。作为热身，我们使用LQG构建了SLE $_κ$的自然参数化，以$κ\ in（4,8）$构建，这可以补充Benoist在Case $κ\ in（0,4）$中的早期工作。
We prove the existence and uniqueness of the canonical conformally covariant volume measure on the carpet/gasket of a conformal loop ensemble (CLE$_κ$, $κ\in (8/3,8)$) which respects the Markov property for CLE. The starting point for the construction is the existence of the canonical measure on CLE in the context of Liouville quantum gravity (LQG) previously constructed by the first author with Sheffield and Werner. As a warm-up, we construct the natural parameterization of SLE$_κ$ for $κ\in (4,8)$ using LQG which serves to complement earlier work of Benoist on the case $κ\in (0,4)$.
