METRIC GLUING OF BROWNIAN AND √8/3-LIOUVILLE QUANTUM GRAVITY SURFACES

• 成果类型: Article
• 署名作者: Gwynne, Ewain; Miller, Jason
• 署名单位: Massachusetts Institute of Technology (MIT); University of Cambridge
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1309
• 发表日期: 2019
• 页码: 2303-2358
• 关键词: planar maps; Scaling Limit; sle

摘要

In a recent series of works, Miller and Sheffield constructed a metric on root 8/3-Liouville quantum gravity (LQG) under which root 8/3-LQG surfaces (e.g., the LQG sphere, wedge, cone and disk) are isometric to their Brownian surface counterparts (e.g., the Brownian map, half-plane, plane and disk). We identify the metric gluings of certain collections of independent root 8/3-LQG surfaces with boundaries identified together according to LQG length along their boundaries. Our results imply in particular that the metric gluing of two independent instances of the Brownian half-plane along their positive boundaries is isometric to a certain LQG wedge decorated by an independent chordal SLE8/3 curve. If one identifies the two sides of the boundary of a single Brownian half-plane, one obtains a certain LQG cone decorated by an independent whole-plane SLE8/3. If one identifies the entire boundaries of two Brownian half-planes, one obtains a different LQG cone and the interface between them is a two-sided variant of whole-plane SLE8/3. Combined with another work of the authors, the present work identifies the scaling limit of self-avoiding walk on random quadrangulations with SLE8/3 on root 8/3-LQG.