Open Access
September 2016 Conformal weldings of random surfaces: SLE and the quantum gravity zipper
Scott Sheffield
Ann. Probab. 44(5): 3474-3545 (September 2016). DOI: 10.1214/15-AOP1055


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.


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Scott Sheffield. "Conformal weldings of random surfaces: SLE and the quantum gravity zipper." Ann. Probab. 44 (5) 3474 - 3545, September 2016.


Received: 1 October 2014; Revised: 1 August 2015; Published: September 2016
First available in Project Euclid: 21 September 2016

zbMATH: 06653523
MathSciNet: MR3551203
Digital Object Identifier: 10.1214/15-AOP1055

Primary: 60D05 , 60K35

Keywords: Conformal welding , Gaussian free field , imaginary geometry , SLE

Rights: Copyright © 2016 Institute of Mathematical Statistics

Vol.44 • No. 5 • September 2016
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