Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals
| dc.creator | Hara, Takashi | |
| dc.date | 2005-04-06 | |
| dc.date | 2008-04-21 | |
| dc.date.accessioned | 2026-07-07T09:33:50Z | |
| dc.date.available | 2026-07-07T09:33:50Z | |
| dc.description | We consider nearest-neighbor self-avoiding walk, bond percolation, lattice trees, and bond lattice animals on ${\mathbb{Z}}^d$. The two-point functions of these models are respectively the generating function for self-avoiding walks from the origin to $x\in{\mathbb{Z}}^d$, the probability of a connection from the origin to $x$, and the generating functions for lattice trees or lattice animals containing the origin and $x$. Using the lace expansion, we prove that the two-point function at the critical point is asymptotic to $\mathit{const.}|x|^{2-d}$ as $|x|\to\infty$, for $d\geq 5$ for self-avoiding walk, for $d\geq19$ for percolation, and for sufficiently large $d$ for lattice trees and animals. These results are complementary to those of [Ann. Probab. 31 (2003) 349--408], where spread-out models were considered. In the course of the proof, we also provide a sufficient (and rather sharp if $d>4$) condition under which the two-point function of a random walk on ${\mathbb{Z}^d}$ is asymptotic to $\mathit{const.}|x|^{2-d}$ as $|x|\to\infty$. | |
| dc.description | Published in at http://dx.doi.org/10.1214/009117907000000231 the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org) | |
| dc.identifier | https://arxiv.org/abs/math-ph/0504021 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0504021 | |
| dc.identifier | Annals of Probability 2008, Vol. 36, No. 2, 530-593 | |
| dc.identifier | doi:10.1214/009117907000000231 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/159276 | |
| dc.subject | Mathematical Physics | |
| dc.subject | 82B27, 82B41, 82B43, 82C41 (Primary) 60K35 (Secondary) | |
| dc.title | Decay of correlations in nearest-neighbor self-avoiding walk, percolation, lattice trees and animals | |
| dc.type | text |