• Corpus ID: 248666042

# The SLE loop via conformal welding of quantum disks

@inproceedings{Ang2022TheSL,
title={The SLE loop via conformal welding of quantum disks},
author={Morris Ang and Nina Holden and Xin Sun},
year={2022}
}
• Published 10 May 2022
• Mathematics
. We prove that the SLE loop measure arises naturally from the conformal welding of two Liouville quantum gravity (LQG) disks for γ 2 = 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 SLE 8…
1 Citations
Integrability of SLE via conformal welding of random surfaces
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We demonstrate how to obtain integrability results for the Schramm-Loewner evolution (SLE) from Liouville conformal field theory (LCFT) and the mating-of-trees framework for Liouville quantum gravity

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