Infinite canonical super-Brownian motion and scaling limits
| dc.creator | van der Hofstad, Remco | |
| dc.date | 2004-05-17 | |
| dc.date.accessioned | 2026-07-07T05:08:21Z | |
| dc.date.available | 2026-07-07T05:08:21Z | |
| dc.description | We construct a measure valued Markov process which we call infinite canonical super-Brownian motion, and which corresponds to the canonical measure of super-Brownian motion conditioned on non-extinction. Infinite canonical super-Brownian motion is a natural candidate for the scaling limit of various random branching objects on $\Z^d$ when these objects are (a) critical; (b) mean-field and (c) infinite. We prove that ICSBM is the scaling limit of the spread-out oriented percolation incipient infinite cluster above 4 dimensions and of incipient infinite branching random walk in any dimension. We conjecture that it also arises as the scaling limit in various other models above the upper-critical dimension, such as the incipient infinite lattice tree above 8 dimensions, the incipient infinite cluster for unoriented percolation, uniform spanning trees above 4 dimensions, and invasion percolation above 6 dimensions. This paper also serves as a survey of recent results linking super-Brownian to scaling limits in statistical mechanics. | |
| dc.description | 34 pages | |
| dc.identifier | https://arxiv.org/abs/math/0405328 | |
| dc.identifier | http://arxiv.org/abs/math/0405328 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/71223 | |
| dc.subject | Probability | |
| dc.title | Infinite canonical super-Brownian motion and scaling limits | |
| dc.type | text |