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First Passage Percolation Has Sublinear Distance Variance

Itai Benjamini·Gil Kalai·Oded Schramm
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Abstract

Let $0 1$ the distance $dist_ω(0,v)$ from the origin to a vertex $v$, $|v|>2$, has variance bounded by $C |v|/\log|v|$, where $C=C(a,b,d)$ is a constant which may only depend on $a$, $b$ and $d$. Some related variants are also discussed

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Itai Benjamini, Gil Kalai, Oded Schramm. 2007-05-25. First Passage Percolation Has Sublinear Distance Variance. https://arxiv.org/abs/math/0203262

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