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• W2923515904 abstract "For $gamma in (0,2)$, the quantum disk and $gamma$-quantum wedge are two of the most natural types of Liouville quantum gravity (LQG) surfaces with boundary. These surfaces arise as scaling limits of finite and infinite random planar maps with boundary, respectively. We show that the left/right quantum boundary length process of a space-filling SLE$_{16/gamma^2}$ curve on a quantum disk or on a $gamma$-quantum wedge is a certain explicit conditioned two-dimensional Brownian motion with correlation $-cos(pigamma^2/4)$. This extends the mating of trees theorem of Duplantier, Miller, and Sheffield (2014) to the case of quantum surfaces with boundary (the disk case for $gamma in (sqrt 2 , 2)$ was previously treated by Duplantier, Miller, Sheffield using different methods). As an application, we give an explicit formula for the conditional law of the LQG area of a quantum disk given its boundary length by computing the law of the corresponding functional of the correlated Brownian motion." @default.
• W2923515904 created "2019-04-01" @default.
• W2923515904 creator A5035621341 @default.
• W2923515904 creator A5074834354 @default.
• W2923515904 date "2019-03-21" @default.
• W2923515904 modified "2023-09-27" @default.
• W2923515904 title "Liouville quantum gravity surfaces with boundary as matings of trees" @default.
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• W2923515904 doi "https://doi.org/10.48550/arxiv.1903.09120" @default.
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