CONFORMAL WELDINGS OF RANDOM SURFACES: SLE AND THE QUANTUM GRAVITY ZIPPER

• 成果类型: Article
• 署名作者: Sheffield, Scott
• 署名单位: Massachusetts Institute of Technology (MIT)
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/15-AOP1055
• 发表日期: 2016
• 页码: 3474-3545
• 关键词: GAUSSIAN MULTIPLICATIVE CHAOS; erased random-walks; SCALING LIMITS; free-field; Invariance; geometry; 2d; UNIVERSALITY; CONVERGENCE; FORMULA

摘要

We construct a conformal welding of two Lionville 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.