{
  "id": "1507.01277",
  "version": "v1",
  "published": "2015-07-05T21:35:59.000Z",
  "updated": "2015-07-05T21:35:59.000Z",
  "title": "Conditional speed of branching Brownian motion, skeleton decomposition and application to random obstacles",
  "authors": [
    "Mehmet Öz",
    "Mine Çağlar",
    "János Engländer"
  ],
  "comment": "32 pages, 1 figure",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study a branching Brownian motion $Z$ in $\\mathbb{R}^d$, among obstacles scattered according to a Poisson random measure with a radially decaying intensity. Obstacles are balls with constant radius and each one works as a trap for the whole motion when hit by a particle. Considering a general offspring distribution, we derive the decay rate of the annealed probability that none of the particles of $Z$ hits a trap, asymptotically in time $t$. This proves to be a rich problem motivating the proof of a more general result about the speed of branching Brownian motion conditioned on non-extinction. We provide an appropriate skeleton decomposition for the underlying Galton-Watson process when supercritical and show through a non-trivial comparison that the doomed particles do not contribute to the asymptotic decay rate.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-07-05T21:35:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J80",
      "60K37",
      "60F10"
    ],
    "keywords": [
      "branching brownian motion",
      "random obstacles",
      "application",
      "conditional",
      "asymptotic decay rate"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 32,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150701277O"
    }
  }
}