On a Lower Bound for the Time Constant of First-Passage Percolation

2008/07/05 by Wu, Xian-Yuan, Feng, Ping
#60K35 #82B43 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Probability (math.PR)

paper · doi:10.48550/arxiv.0807.0839

Abstract

We consider the Bernoulli first-passage percolation on \mathbb Z^d (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

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