A lower bound for the chemical distance in sparse long-range percolation models
| dc.creator | Berger, Noam | |
| dc.date | 2004-09-01 | |
| dc.date.accessioned | 2026-07-07T05:11:44Z | |
| dc.date.available | 2026-07-07T05:11:44Z | |
| dc.description | We consider long-range percolation in dimension $d\geq 1$, where distinct sites $x$ and $y$ are connected with probability $p_{x,y}\in[0,1]$. Assuming that $p_{x,y}$ is translation invariant and that $p_{x,y}=\|x-y\|^{-s+o(1)}$ with $s>2d$, we show that the graph distance is at least linear with the Euclidean distance. | |
| dc.description | 9 pages | |
| dc.identifier | https://arxiv.org/abs/math/0409021 | |
| dc.identifier | http://arxiv.org/abs/math/0409021 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/72345 | |
| dc.subject | Probability | |
| dc.subject | 60K35; 82B43, 82B28 | |
| dc.title | A lower bound for the chemical distance in sparse long-range percolation models | |
| dc.type | text |