Chordal SLE$_6$ explorations of a quantum disk

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 $η$ between its marked boundary points. We obtain descriptions of the law of the quantum surfaces parameterized by the complementary connected components of $η([0,t])$ for each time $t \geq 0$ as well as the law of the left/right $\sqrt{8/3}$-quantum boundary length process for $η$.

21 pages, 3 figures; final version, to appear in EJP