GEODESICS IN FIRST PASSAGE PERCOLATION

• 成果类型: Article
• 署名作者: Hoffman, Christopher
• 署名单位: University of Washington; University of Washington Seattle
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/07-AAP510
• 发表日期: 2008
• 页码: 1944-1969
• 关键词: increasing subsequences; coexistence; models

摘要

We consider a wide class of ergodic first passage percolation processes on Z(2) and prove that there exist at least four one-sided geodesics a.s. We also show that coexistence is possible with positive probability in a four-color Richardson's growth model. This improves earlier results of Haggstrom and Pemantle [J. Appl. Prohah. 35 (1995) 683-692]. Garet and Marchand [Ann. Appl. Probah. 15 (2005) 298-330] and Hoffman [Ann. Appl. Probab. 15 (2005) 739-747] who proved that first passage percolation has at least two geodesics and that coexistence is possible in a two-color Richardson's growth model.