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Date
2023Type
- Journal Article
ETH Bibliography
yes
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Abstract
Two-pointed quantum disks with a weight parameter W>0 are a family of finite-area random surfaces that arise naturally in Liouville quantum gravity. In this paper we show that conformally welding two quantum disks according to their boundary lengths gives another quantum disk decorated with an independent chordal SLEκ(ρ−;ρ+) curve. This is the finite-volume counterpart of the classical result of Sheffield (2010) and Duplantier-Miller-Sheffield (2014) on the welding of infinite-area two-pointed quantum surfaces called quantum wedges, which is fundamental to the mating-of-trees theory. Our results can be used to give unified proofs of the mating-of-trees theorems for the quantum disk and the quantum sphere, in addition to a mating-of-trees description of the weight W=γ2/2 quantum disk. Moreover, it serves as a key ingredient in our companion work, which proves an exact formula for SLEκ(ρ−;ρ+) using conformal welding of random surfaces and a conformal welding result giving the so-called SLE loop. Show more
Permanent link
https://doi.org/10.3929/ethz-b-000611690Publication status
publishedExternal links
Journal / series
Electronic Journal of ProbabilityVolume
Pages / Article No.
Publisher
Institute of Mathematical StatisticsSubject
Schramm-Loewner evolution; Liouville quantum gravityMore
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ETH Bibliography
yes
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