Reversibility of whole-plane SLE for K>8

• 成果类型: Article; Early Access
• 署名作者: Ang, Morris; Yu, Pu
• 署名单位: University of California System; University of California San Diego; New York University
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-024-01333-w
• 发表日期: 2024
• 关键词: liouville quantum-gravity; erased random-walks; conformal-invariance; SURFACES; matings; trees; MAPS

摘要

Whole-plane Schramm-Loewner evolution (SLE kappa) is a random fractal curve betweentwo points on the Riemann sphere. Zhan established for kappa <= 4 that whole-plane SLE kappa isreversible, meaning invariant in law under conformal automorphisms swapping itsendpoints. Miller and Sheffield extended this to kappa <= 8. We prove whole-plane SLE kappa is reversible for kappa>8, resolving the final case and answering a conjecture of Viklundand Wang. Our argument depends on a novel mating-of-trees theorem of independentinterest, where Liouville quantum gravity on the disk is decorated by an independentradial space-filling SLE curve.