共形环系综上的共形协变体积测度的存在性与唯一性
Existence and uniqueness of the conformally covariant volume measure on conformal loop ensembles
AI总结：
本文证明了共形环系综（CLE）上共形协变体积测度的存在性与唯一性，并利用Liouville量子引力构造了SLE的自然参数化，补充了先前研究。
摘要：
我们证明了在共形环系综（CLE$_κ$，$κ\in (8/3,8)$）的carpet/gasket上存在且唯一的典范共形协变体积测度，该测度尊重CLE的马尔可夫性质。构造的起点是Liouville量子引力（LQG）背景下CLE上典范测度的存在性，该测度由第一作者与Sheffield和Werner先前构造。作为热身，我们利用LQG构造了SLE$_κ$（$κ\in (4,8)$）的自然参数化，这补充了Benoist关于$κ\in (0,4)$情形的早期工作。
英文摘要：
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 $κ\in (0,4)$.
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