LIMIT THEOREMS FOR 2D INVASION PERCOLATION

• 成果类型: Article
• 署名作者: Damron, Michael; Sapozhnikov, Artem
• 署名单位: Princeton University; Swiss Federal Institutes of Technology Domain; ETH Zurich
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/10-AOP641
• 发表日期: 2012
• 页码: 893-920
• 关键词: porous-media; dimensions

摘要

We prove limit theorems and variance estimates for quantities related to ponds and outlets for 2D invasion percolation. We first exhibit several properties of a sequence (O(n)) of outlet variables, the nth of which gives the number of outlets in the box centered at the origin of side length 2(n). The most important of these properties describes the sequence's renewal structure and exponentially fast mixing behavior. We use these to prove a central limit theorem and strong law of large numbers for (O(n)). We then show consequences of these limit theorems for the pond radii and outlet weights.