The Center of Mass for Spatial Branching Processes and an Application for Self-Interaction
| dc.creator | Englander, Janos | |
| dc.date | 2008-08-29 | |
| dc.date.accessioned | 2026-07-07T09:59:25Z | |
| dc.date.available | 2026-07-07T09:59:25Z | |
| dc.description | In this paper we prove that the center of mass of a supercritical branching-Brownian motion, or that of a supercritical super-Brownian motion tends to a limiting position almost surely, which, in a sense complements a result of Tribe on the final behavior of a critical super-Brownian motion. This is shown to be true also for a model where branching Brownian motion is modified by attraction/repulsion between particles. We then put this observation together with the description of the interacting system as viewed from its center of mass, and get the following asymptotic behavior: the system asymptotically becomes a branching Ornstein Uhlenbeck process (inward for attraction and outward for repulsion), but the origin is shifted to a random point which has normal distribution, and the Ornstein Uhlenbeck particles are not independent but constitute a system with a degree of freedom which is less by their number by precisely one. | |
| dc.identifier | https://arxiv.org/abs/0808.4024 | |
| dc.identifier | http://arxiv.org/abs/0808.4024 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/168013 | |
| dc.subject | Probability | |
| dc.subject | 60J60; 60J80 | |
| dc.title | The Center of Mass for Spatial Branching Processes and an Application for Self-Interaction | |
| dc.type | text |