考虑Zd(d≥2)上的Bernoulli首达渗流,即模型的边通过时间独立地以概率1-P取值为1,以概率P取值为0.记μ(p)为模型的时间常数.本文使用Russo公式证明,对任意0≤p1〈p2〈1, μ(p1)-μ(p2)≥μ(p2)/1-p2(p2-p1).
We consider the Bernoulli first-passage percolation on Zd (d ≥ 2). That is, the edge passage time is taken independently to be 1 with probability 1 -p and 0 otherwise. Let μ(p) be the time constant. We prove in this paper that μ(p1)-μ(p2)≥μ(p2)/1-p2(p2-p1). for all 0 ≤ p1 〈 p2 〈 1 by using Russo's formula.