N-sided radial Schramm-Loewner evolution

• 成果类型: Article
• 署名作者: Healey, Vivian Olsiewski; Lawler, Gregory F.
• 署名单位: University of Chicago; Texas State University System; Texas State University San Marcos
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-021-01033-9
• 发表日期: 2021
• 页码: 451-488
• 关键词: erased random-walks

摘要

We use the interpretation of the Schramm-Loewner evolution as a limit of path measures tilted by a loop term in order to motivate the definition of n-radial SLE going to a particular point. In order to justify the definition we prove that the measure obtained by an appropriately normalized loop term on n-tuples of paths has a limit. The limit measure can be described as n paths moving by the Loewner equation with a driving term of Dyson Brownian motion. While the limit process has been considered before, this paper shows why it naturally arises as a limit of configurational measures obtained from loop measures.