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arXiv · 1701.05172

Chordal SLE$_6$ explorations of a quantum disk

Ewain Gwynne·Jason Miller
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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 $η$.

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Ewain Gwynne, Jason Miller. 2018-07-01. Chordal SLE$_6$ explorations of a quantum disk. https://arxiv.org/abs/1701.05172

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