Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation
| dc.creator | Chen, Lung-Chi | |
| dc.creator | Sakai, Akira | |
| dc.date | 2008-04-13 | |
| dc.date | 2008-08-11 | |
| dc.date.accessioned | 2026-07-07T09:55:35Z | |
| dc.date.available | 2026-07-07T09:55:35Z | |
| dc.description | We prove that the Fourier transform of the properly-scaled normalized two-point function for sufficiently spread-out long-range oriented percolation with index α>0 converges to e^{-C|k|^{α\wedge2}} for some C\in(0,\infty) above the upper-critical dimension 2(α\wedge2). This answers the open question remained in the previous paper [arXiv:math/0703455]. Moreover, we show that the constant C exhibits crossover at α=2, which is a result of interactions among occupied paths. The proof is based on a new method of estimating fractional moments for the spatial variable of the lace-expansion coefficients. | |
| dc.description | 20 pages, 1 figure | |
| dc.identifier | https://arxiv.org/abs/0804.2039 | |
| dc.identifier | http://arxiv.org/abs/0804.2039 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/166679 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35; 82B27 | |
| dc.title | Critical behavior and the limit distribution for long-range oriented percolation. II: Spatial correlation | |
| dc.type | text |