# Chordal SLE$_6$ explorations of a quantum disk

## TL;DR

This paper studies the interaction between chordal SLE$_6$ curves and doubly marked quantum disks in Liouville quantum gravity, providing detailed descriptions of the resulting quantum surfaces and boundary length processes.

## Contribution

It offers new probabilistic descriptions of quantum surfaces and boundary length dynamics in the setting of SLE$_6$ on quantum disks, advancing understanding of quantum gravity surfaces.

## Key findings

- Law of quantum surfaces parameterized by SLE$_6$ components
- Distribution of boundary length processes for SLE$_6$
- Descriptions of quantum surface laws conditioned on SLE$_6$ exploration

## Abstract

We consider a particular type of $\sqrt{8/3}$-Liouville quantum gravity surface called a doubly marked quantum disk (equivalently, a Brownian disk) decorated by an independent chordal SLE$_6$ curve $\eta$ between its marked boundary points. We obtain descriptions of the law of the quantum surfaces parameterized by the complementary connected components of $\eta([0,t])$ for each time $t \geq 0$ as well as the law of the left/right $\sqrt{8/3}$-quantum boundary length process for $\eta$.