The SLE loop via conformal welding of quantum disks

Morris Ang, Nina Holden, Xin Sun

Research output: Contribution to journalArticlepeer-review


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 languageEnglish (US)
Article number30
JournalElectronic Journal of Probability
StatePublished - 2023


  • Liouville quantum gravity
  • Schramm-Loewner evolution

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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