{
  "id": "0808.4024",
  "version": "v1",
  "published": "2008-08-29T05:25:51.000Z",
  "updated": "2008-08-29T05:25:51.000Z",
  "title": "The Center of Mass for Spatial Branching Processes and an Application for Self-Interaction",
  "authors": [
    "Janos Englander"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2008-08-29T05:25:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J80"
    ],
    "keywords": [
      "spatial branching processes",
      "application",
      "self-interaction",
      "branching ornstein uhlenbeck process",
      "ornstein uhlenbeck particles"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2008arXiv0808.4024E"
    }
  }
}