{
  "id": "1305.6723",
  "version": "v1",
  "published": "2013-05-29T08:39:26.000Z",
  "updated": "2013-05-29T08:39:26.000Z",
  "title": "Scaling limit of the path leading to the leftmost particle in a branching random walk",
  "authors": [
    "Xinxin Chen"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a discrete-time branching random walk defined on the real line, which is assumed to be supercritical and in the boundary case. It is known that its leftmost position of the $n$-th generation behaves asymptotically like $\\frac{3}{2}\\ln n$, provided the non-extinction of the system. The main goal of this paper, is to prove that the path from the root to the leftmost particle, after a suitable normalizatoin, converges weakly to a Brownian excursion in $D([0,1],\\r)$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-05-29T08:39:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "leftmost particle",
      "scaling limit",
      "path leading",
      "discrete-time branching random walk"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1305.6723C"
    }
  }
}