Gouéré, Jean-Baptiste Monotonicity in first-passage percolation. (English) Zbl 1301.60108 ALEA, Lat. Am. J. Probab. Math. Stat. 11, No. 2, 565-569 (2014). Summary: We consider standard first-passage percolation on \(\mathbb Z^d\). Let \(e_1\) be the first coordinate vector. Let \(a(n)\) be the expected passage time from the origin to \(ne_1\). In this short paper, we note that \(a(n)\) is increasing under some strong condition on the support of the distribution of the passage times on the edges. Cited in 4 Documents MSC: 60K35 Interacting random processes; statistical mechanics type models; percolation theory 82B43 Percolation Keywords:first-passage percolation PDFBibTeX XMLCite \textit{J.-B. Gouéré}, ALEA, Lat. Am. J. Probab. Math. Stat. 11, No. 2, 565--569 (2014; Zbl 1301.60108) Full Text: arXiv