Nondifferentiability of the time constants of first-passage percolation

• 成果类型: Article
• 署名作者: Steele, JM; Zhang, Y
• 署名单位: University of Pennsylvania; University of Colorado System; University of Colorado at Colorado Springs
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• 发表日期: 2003
• 页码: 1028-1051
• 关键词: 1st-passage percolation

摘要

We study the paths of minimal cost for first-passage percolation in two dimensions and obtain an exponential bound on the tail probability of the ratio of the lengths of the shortest and longest of these. This inequality permits us to answer a long-standing question of Hammersley and Welsh on the shift differentiability of the time constant. Specifically, we show that for subcritical Bernoulli percolation the time constant is not shift differentiable when p is close to one-half.