SLE Loop Measure and Liouville Quantum Gravity

Understand

As recently shown by Holden and two of the authors, the conformal welding of two Liouville quantum gravity (LQG) disks produces a canonical variant of SLE curve whose law is called the SLE loop measure.

• In this paper, we demonstrate how LQG can be used to study the SLE loop measure.
• Firstly, we show that for $\kappa\in (8/3,8)$, the loop intensity measure of the conformal loop ensemble agrees with the SLE loop measure as defined by Zhan (2021).
• The former was initially considered by Kemppainen and Werner (2016) for $\kappa\in (8/3,4]$, and the latter was constructed for $\kappa\in (0,8)$.