Singularity points for first passage percolation

• 成果类型: Article
• 署名作者: Yukich, JE; Zhang, Y
• 署名单位: Lehigh University; University of Colorado System; University of Colorado at Colorado Springs
• 刊物名称: ANNALS OF PROBABILITY
• ISSN/ISSBN: 0091-1798
• DOI: 10.1214/009117905000000819
• 发表日期: 2006
• 页码: 577-592
• 关键词: supercritical oriented percolation; time constant; right edge

摘要

Let 0 < a < b < infinity be fixed scalars. Assign independently to each edge in the lattice Z(2) the value a with probability p or the value b with probability 1 - p. For all u, v is an element of Z(2), let T(u, v) denote the first passage time between u and v. We show that there are points x is an element of R-2 such that the time constant in the direction of x, namely, lim(n ->infinity) n(-1) E-p[T(0, nx)], is not a three times differentiable function of p.