First Passage Percolation Has Sublinear Distance Variance

Details First Passage Percolation Has Sublinear Distance Variance First Passage Percolation Has Sublinear Distance Variance

2002-03-25

arxiv.org/abs/math/0203262v5

AnnalsProbab.31:197-1978,2003

Mathematics

Probability

Replaced theorem 2 (which was incorrect) by a new theorem

Scientific paper

Let $01$ the distance $dist_\omega(0,v)$ 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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