论文标题
通过量子磁盘的共形焊接的SLE环
The SLE loop via conformal welding of quantum disks
论文作者
论文摘要
我们证明，SLE $_κ$循环度量自然来自两个$γ$ -liouville量子重力（LQG）磁盘的共形焊接，以$γ^2 =κ\ in（0,4）$。证明依赖于我们的同伴工作在LQG磁盘的保形焊接方面，并用作必不可少的工具，即LQG表面均匀嵌入的概念。将我们的结果与Gwynne和Miller的作品相结合，我们得到了通过避免自我的多边形装饰的随机四边形，以缩放限制将SLE $ _ {8/3} $环装饰的LQG球体汇总到LQG球体。我们的结果也是第一和第三名合着者在共同循环集合的整合性方面的最新工作的关键输入。
We prove that the SLE$_κ$ loop measure arises naturally from the conformal welding of two $γ$-Liouville quantum gravity (LQG) disks for $γ^2 = κ\in (0,4)$. The proof relies on our companion work on conformal welding of LQG disks and uses as an essential tool the concept of uniform embedding of LQG surfaces. Combining our result with work of Gwynne and Miller, we get that random quadrangulations decorated by a self-avoiding polygon converge in the scaling limit to the LQG sphere decorated by the SLE$_{8/3}$ loop. Our result is also a key input to recent work of the first and third coauthors on the integrability of the conformal loop ensemble.
