Nina Holden
Conformal welding for critical Liouville quantum gravity
Holden, Nina; Powell, Ellen
Abstract
Consider two critical Liouville quantum gravity surfaces (i.e., γ-LQG for γ = 2), each with the topology of H and with infinite boundary length. We prove that there a.s. exists a conformal welding of the two surfaces, when the boundaries are identified according to quantum boundary length. This results in a critical LQG surface decorated by an independent SLE4. Combined with the proof of uniqueness for such a welding, recently established by McEnteggart, Miller, and Qian (2018), this shows that the welding operation is well-defined. Our result is a critical analogue of Sheffield’s quantum gravity zipper theorem (2016), which shows that a similar conformal welding for subcritical LQG (i.e., γ-LQG for γ ∈ (0, 2)) is well-defined.
Citation
Holden, N., & Powell, E. (2021). Conformal welding for critical Liouville quantum gravity. Annales de l'Institut Henri Poincaré, Probabilités et Statistiques, 57(3), 1229-1254. https://doi.org/10.1214/20-aihp1116
Journal Article Type | Article |
---|---|
Acceptance Date | Oct 22, 2020 |
Online Publication Date | Jul 22, 2021 |
Publication Date | 2021-08 |
Deposit Date | Dec 9, 2020 |
Publicly Available Date | Aug 5, 2021 |
Journal | Annales de l'Institut Henri Poincaré, Probabilités et Statistiques |
Print ISSN | 0246-0203 |
Publisher | Institute of Mathematical Statistics |
Peer Reviewed | Peer Reviewed |
Volume | 57 |
Issue | 3 |
Pages | 1229-1254 |
DOI | https://doi.org/10.1214/20-aihp1116 |
Related Public URLs | https://arxiv.org/abs/1812.11808 |
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