The Brownian loop soup

• 成果类型: Article
• 署名作者: Lawler, GF; Werner, W
• 署名单位: Cornell University; Universite Paris Saclay
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-003-0319-6
• 发表日期: 2004
• 页码: 565-588
• 关键词: conformal restriction; REPRESENTATIONS

摘要

We define a natural conformally invariant measure on unrooted Brownian loops in the plane and study some of its properties. We relate this measure to a measure on loops rooted at a boundary point of a domain and show how this relation gives a way to chronologically add Brownian loops to simple curves in the plane.