Monotonicity in first-passage percolation

Details Monotonicity in first-passage percolation Monotonicity in first-passage percolation

2012-02-13

arxiv.org/abs/1202.2665v1

Mathematics

Probability

Scientific paper

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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