Abstract
We prove that the SLEκ loop measure arises naturally from the conformal welding of two γ-Liouville quantum gravity (LQG) disks for γ2 = κ ∈ (0, 4). The proof relies on our companion work on conformal welding of LQG disks and uses as an essential tool the concept of uniform embedding of LQG surfaces. Combining our result with work of Gwynne and Miller, we get that random quadrangulations decorated by a self-avoiding polygon converge in the scaling limit to the LQG sphere decorated by the SLE8/3 loop. Our result is also a key input to recent work of the first and third coauthors on the integrability of the conformal loop ensemble.
Original language | English (US) |
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Article number | 30 |
Journal | Electronic Journal of Probability |
Volume | 28 |
DOIs | |
State | Published - 2023 |
Keywords
- Liouville quantum gravity
- Schramm-Loewner evolution
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty