Critical behavior and the limit distribution for long-range oriented percolation. I
| dc.creator | Chen, Lung-Chi | |
| dc.creator | Sakai, Akira | |
| dc.date | 2007-03-15 | |
| dc.date | 2007-08-21 | |
| dc.date.accessioned | 2026-07-07T08:24:31Z | |
| dc.date.available | 2026-07-07T08:24:31Z | |
| dc.description | We consider oriented percolation on Z^d times Z_+ whose bond-occupation probability is pD(...), where p is the percolation parameter and D is a probability distribution on Z^d. Suppose that D(x) decays as |x|^{-d-α} for some α>0. We prove that the two-point function obeys an infrared bound which implies that various critical exponents take on their respective mean-field values above the upper-critical dimension 2\min{α,2}. We also show that, for every k, the Fourier transform of the normalized two-point function at time n, with a proper spatial scaling, has a convergent subsequence to exp(-c|k|^{\min{α,2}}) for some c>0. | |
| dc.description | 33 pages, 2 figures | |
| dc.identifier | https://arxiv.org/abs/math/0703455 | |
| dc.identifier | http://arxiv.org/abs/math/0703455 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/136365 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35, 82B27 | |
| dc.title | Critical behavior and the limit distribution for long-range oriented percolation. I | |
| dc.type | text |