CLASSIFICATION OF SCALING LIMITS OF UNIFORM QUADRANGULATIONS WITH A BOUNDARY

• 成果类型: Article
• 署名作者: Baur, Erich; Miermont, Gregory; Ray, Gourab
• 署名单位: Ecole Normale Superieure de Lyon (ENS de LYON); University of Victoria
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/18-AOP1316
• 发表日期: 2019
• 页码: 3397-3477
• 关键词: planar maps; geodesics

摘要

We study noncompact scaling limits of uniform random planar quadran-gulations with a boundary when their size tends to infinity. Depending on the asymptotic behavior of the boundary size and the choice of the scaling factor, we observe different limiting metric spaces. Among well-known objects like the Brownian plane or the self-similar continuum random tree, we construct two new one-parameter families of metric spaces that appear as scaling limits: the Brownian half-plane with skewness parameter theta and the infinite-volume Brownian disk of perimeter sigma. We also obtain various coupling and limit results clarifying the relation between these objects.