## Electronic Journal of Probability

### 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 $\eta$ 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 $\eta$.

#### Article information

Source
Electron. J. Probab., Volume 23 (2018), paper no. 66, 24 pp.

Dates
Accepted: 22 March 2018
First available in Project Euclid: 26 July 2018

https://projecteuclid.org/euclid.ejp/1532570594

Digital Object Identifier
doi:10.1214/18-EJP161

Mathematical Reviews number (MathSciNet)
MR3835472

Zentralblatt MATH identifier
06924678

#### Citation

Gwynne, Ewain; Miller, Jason. Chordal SLE$_6$ explorations of a quantum disk. Electron. J. Probab. 23 (2018), paper no. 66, 24 pp. doi:10.1214/18-EJP161. https://projecteuclid.org/euclid.ejp/1532570594

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