Peeling the Brownian half-plane

• 成果类型: Article; Early Access
• 署名作者: Le Gall, Jean-Francois; Riera, Armand
• 署名单位: Universite Paris Saclay; Sorbonne Universite; Universite Paris Cite
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-025-01427-z
• 发表日期: 2025
• 关键词: maps

摘要

We establish a new spatial Markov property of the Brownian half-plane. According to this property, if one removes a hull centered at a boundary point, the remaining space equipped with an intrinsic metric is still a Brownian half-plane, which is independent of the part that has been removed. This is an analog of the well-known peeling procedure for random planar maps. We also investigate several distributional properties of hulls centered at a boundary point, and we provide a new construction of the Brownian half-plane giving information about distances from a half-boundary.