Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: I. The higher-point functions
| dc.creator | van der Hofstad, Remco | |
| dc.creator | Sakai, Akira | |
| dc.date | 2008-09-10 | |
| dc.date.accessioned | 2026-07-07T10:01:57Z | |
| dc.date.available | 2026-07-07T10:01:57Z | |
| dc.description | We consider the critical spread-out contact process in Z^d with d\ge1, whose infection range is denoted by L\ge1. In this paper, we investigate the r-point function τ_{\vec t}^{(r)}(\vec x) for r\ge3, which is the probability that, for all i=1,...,r-1, the individual located at x_i\in Z^d is infected at time t_i by the individual at the origin o\in Z^d at time 0. Together with the results of the 2-point function in [van der Hofstad and Sakai, Electron. J. Probab. 9 (2004), 710-769; arXiv:math/0402049], on which our proofs crucially rely, we prove that the r-point functions converge to the moment measures of the canonical measure of super-Brownian motion above the upper-critical dimension 4. We also prove partial results for d\le4 in a local mean-field setting. | |
| dc.description | 75 pages, 12 figures | |
| dc.identifier | https://arxiv.org/abs/0809.1712 | |
| dc.identifier | http://arxiv.org/abs/0809.1712 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168809 | |
| dc.subject | Probability | |
| dc.subject | Mathematical Physics | |
| dc.subject | 60K35 (Primary) 82B27, 82B43 (Secondary) | |
| dc.title | Convergence of the critical finite-range contact process to super-Brownian motion above the upper critical dimension: I. The higher-point functions | |
| dc.type | text |