SCALING LIMIT OF THE INVASION PERCOLATION CLUSTER ON A REGULAR TREE

• 成果类型: Article
• 署名作者: Angel, Omer; Goodman, Jesse; Merle, Mathieu
• 署名单位: University of British Columbia; Leiden University - Excl LUMC; Leiden University; Universite Paris Cite
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/11-AOP731
• 发表日期: 2013
• 页码: 229-261
• 关键词: incipient infinite cluster

摘要

We prove existence of the scaling limit of the invasion percolation cluster (IPC) on a regular tree. The limit is a random real tree with a single end. The contour and height functions of the limit are described as certain diffusive stochastic processes. This convergence allows us to recover and make precise certain asymptotic results for the MC. In particular, we relate the limit of the rescaled level sets of the MC to the local time of the scaled height function.