Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions
| dc.creator | van der Hofstad, Remco | |
| dc.creator | Sakai, Akira | |
| dc.date | 2004-02-04 | |
| dc.date | 2004-09-24 | |
| dc.date.accessioned | 2026-07-07T05:05:06Z | |
| dc.date.available | 2026-07-07T05:05:06Z | |
| dc.description | We consider self-avoiding walk and percolation in $\Zd$, oriented percolation in $\Zd\times\Zp$, and the contact process in $\Zd$, with $p D(\cdot)$ being the coupling function whose range is denoted by $L<\infty$. For percolation, for example, each bond $\{x,y\}$ is occupied with probability $p D(y-x)$. The above models are known to exhibit a phase transition when the parameter $p$ varies around a model-dependent critical point $\pc$. We investigate the value of $\pc$ when $d>6$ for percolation and $d>4$ for the other models, and $L\gg1$. We prove in a unified way that $\pc=1+C(D)+O(L^{-2d})$, where the universal term 1 is the mean-field critical value, and the model-dependent term $C(D)=O(L^{-d})$ is written explicitly in terms of the function $D$. Our proof is based on the lace expansion for each of these models. | |
| dc.description | 22 pages, no figures | |
| dc.identifier | https://arxiv.org/abs/math/0402050 | |
| dc.identifier | http://arxiv.org/abs/math/0402050 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/70053 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.title | Critical points for spread-out self-avoiding walk, percolation and the contact process above the upper critical dimensions | |
| dc.type | text |