# Monotonicity in first-passage percolation

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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https://hal.archives-ouvertes.fr/hal-00669299
Contributor : Jean-Baptiste Gouéré <>
Submitted on : Wednesday, October 3, 2012 - 6:00:07 PM
Last modification on : Thursday, May 3, 2018 - 3:32:06 PM
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HAL-fpp-monotonie2.pdf
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• HAL Id : hal-00669299, version 2
• ARXIV : 1202.2665

### Citation

Jean-Baptiste Gouéré. Monotonicity in first-passage percolation. ALEA : Latin American Journal of Probability and Mathematical Statistics, Instituto Nacional de Matemática Pura e Aplicada, 2014, pp.11(2):565-569. ⟨hal-00669299v2⟩

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