Absence of geodesics in first-passage percolation on a half-plane

• 成果类型: Article
• 署名作者: Wehr, J; Woo, J
• 署名单位: University of Arizona; University of Arizona
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 1998
• 页码: 358-367
• 关键词: 1st-passage percolation

摘要

An H-geodesic is a doubly infinite path which locally minimizes the passage time in the i.i.d. first passage percolation model on a half-plane H. Under the assumption that the bond passage times are continuously distributed with a finite mean, we prove that, with probability 1, H-geodesics do not exist. As a corollary we show that, with probability 1, any geodesic in the analogous model on the whole plane Z(2) has to intersect all straight lines with rational slopes.