A geometrical structure for an infinite oriented cluster and its uniqueness

• 成果类型: Article
• 署名作者: Wu, Xian-Yuan; Zuang, Yu
• 署名单位: Capital Normal University; University of Colorado System; University of Colorado at Colorado Springs
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/07-AOP339
• 发表日期: 2008
• 页码: 862-875
• 关键词: brownian web; poisson trees; right edge; percolation; dimensions

摘要

We consider the supercritical oriented percolation model. Let K be all the percolation points. For each u is an element of K, we write Y-u as its rightmost path. Let G = U-u y(u). In this paper, we show that G is a single tree with only one topological end. We also present a relationship between X and G and construct a bijection between K and Z using the preorder traversal algorithm. Through applications of this fundamental graph property, we show the uniqueness of an infinite oriented cluster by ignoring finite vertices.