Conformal weldings of random surfaces: SLE and the quantum gravity zipper

Scott Sheffield

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arXiv · 1012.4797

Conformal weldings of random surfaces: SLE and the quantum gravity zipper

Scott Sheffield

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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.

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math.PR cond-mat.stat-mech math-ph math.CV math.MP

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Scott Sheffield. 2010-12-21. Conformal weldings of random surfaces: SLE and the quantum gravity zipper. https://arxiv.org/abs/1012.4797

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