First Passage Percolation Has Sublinear Distance Variance
| dc.creator | Benjamini, Itai | |
| dc.creator | Kalai, Gil | |
| dc.creator | Schramm, Oded | |
| dc.date | 2002-03-25 | |
| dc.date | 2007-05-25 | |
| dc.date.accessioned | 2026-07-07T10:22:30Z | |
| dc.date.available | 2026-07-07T10:22:30Z | |
| dc.description | Let $0<a<b<\infty$, and for each edge $e$ of $Z^d$ let $ω_e=a$ or $ω_e=b$, each with probability 1/2, independently. This induces a random metric $\dist_ω$ on the vertices of $Z^d$, called first passage percolation. We prove that for $d>1$ 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 | |
| dc.description | Replaced theorem 2 (which was incorrect) by a new theorem | |
| dc.identifier | https://arxiv.org/abs/math/0203262 | |
| dc.identifier | http://arxiv.org/abs/math/0203262 | |
| dc.identifier | AnnalsProbab.31:197-1978,2003 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/175533 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35; 60B15 | |
| dc.title | First Passage Percolation Has Sublinear Distance Variance | |
| dc.type | text |