Conformal weldings of random surfaces: SLE and the quantum gravity zipper
Name
1012.4797.pdf
Size
1.02 MB
Format
Adobe PDF
Checksum (MD5)
ebed48c1b6c851ea15feee430e1f7084
Author(s)
Sheffield, Scott Roger
Date Issued
September 2016
Journal
The Annals of Probability
Publisher
Institute of Mathematical Statistics
Citation
Sheffield, Scott. “Conformal Weldings of Random Surfaces: SLE and the Quantum Gravity Zipper.” The Annals of Probability 44, 5 (September 2016): 3474–3545
Version
Original manuscript
Abstract
We construct a conformal welding of two Liouville quantum gravity random surfaces and show that the interface between them is a random fractal curve called the Schramm–Loewner evolution (SLE), thereby resolving a variant of a conjecture of Peter Jones. We also demonstrate some surprising symmetries of this construction, which are consistent with the belief that (path-decorated) random planar maps have (SLE-decorated) Liouville quantum gravity as a scaling limit. We present several precise conjectures and open questions.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
Creative Commons Attribution-Noncommercial-Share Alike
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1214/15-AOP1055
