Scaling limits for planar aggregation with subcritical fluctuations

• 成果类型: Article
• 署名作者: Norris, James; Silvestri, Vittoria; Turner, Amanda
• 署名单位: University of Cambridge; Sapienza University Rome; University of Leeds
• 刊物名称: PROBABILITY THEORY AND RELATED FIELDS
• ISSN/ISSBN: 0178-8051
• DOI: 10.1007/s00440-022-01141-0
• 发表日期: 2023
• 页码: 185-250
• 关键词: random growth

摘要

We study scaling limits of a family of planar random growth processes in which clusters grow by the successive aggregation of small particles. In these models, clusters are encoded as a composition of conformal maps and the location of each successive particle is distributed according to the density of harmonic measure on the cluster boundary, raised to some power. We show that, when this power lies within a particular range, the macroscopic shape of the cluster converges to a disk, but that as the power approaches the edge of this range the fluctuations approach a critical point, which is a limit of stability. The methodology developed in this paper provides a blueprint for analysing more general random growth models, such as the Hastings-Levitov family.