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arXiv · 1202.2665

Monotonicity in first-passage percolation

Jean-Baptiste Gouéré
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Abstract

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.

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Jean-Baptiste Gouéré. 2012-02-13. Monotonicity in first-passage percolation. https://arxiv.org/abs/1202.2665

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