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

• Scott Sheffield ^[1]
  1. [1] Massachusetts Institute of Technology

     Massachusetts Institute of Technology

     City of Cambridge, Estados Unidos

     
• Localización: Annals of probability: An official journal of the Institute of Mathematical Statistics, ISSN 0091-1798, Vol. 44, Nº. 5, 2016, págs. 3474-3545
• Idioma: inglés
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• Resumen

  • 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.