Monotonicity in first-passage percolation

Jean-Baptiste Gouéré

Published 2012-02-13, updated 2012-10-04Version 2

We consider standard first-passage percolation on $\Z^d$. 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 law of the passage times on the edges.