Asymptotic shapes for stationary first passage percolation

• 成果类型: Article
• 署名作者: Haggstrom, O; Meester, R
• 署名单位: Utrecht University
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/aop/1176987792
• 发表日期: 1995
• 页码: 1511-1522
• 关键词: theorems

摘要

This paper deals with first passage percolation where the usual i.i.d. condition is weakened to stationarity (and ergodicity). The well known asymptotic shape result is known to extend to this case. It is easy to give necessary conditions for a compact set B subset of R(d) to arise as the asymptotic shape for some stationary measure on the passage times. Our main result says that these conditions are also sufficient.