{
  "id": "1712.08979",
  "version": "v1",
  "published": "2017-12-25T00:59:06.000Z",
  "updated": "2017-12-25T00:59:06.000Z",
  "title": "The Minimal Position of a Stable Branching Random Walk",
  "authors": [
    "Jingning Liu",
    "Mei Zhang"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper, a branching random walk $(V(x))$ in the boundary case is studied, where the associated one dimensional random walk is in the domain of attraction of an $\\alpha-$stable law with $1<\\alpha<2$. Let $M_n$ be the minimal position of $(V(x))$ at generation $n$. We established an integral test to describe the lower limit of $M_n-\\frac{1}{\\alpha}\\log n$ and a law of iterated logarithm for the upper limit of $M_n-(1+\\frac{1}{\\alpha})\\log n$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-12-25T00:59:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "stable branching random walk",
      "minimal position",
      "dimensional random walk",
      "lower limit",
      "boundary case"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}