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

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

2010-12-21

arxiv.org/abs/1012.4797v1

Mathematics

Probability

83 pages, 22 figures

Scientific paper

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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