{
  "id": "1610.08151",
  "version": "v1",
  "published": "2016-10-26T02:37:10.000Z",
  "updated": "2016-10-26T02:37:10.000Z",
  "title": "Monotonicity of the speed for biased random walk on Galton-Watson tree",
  "authors": [
    "Song He",
    "Wang Longmin",
    "Xiang Kainan"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Ben Arous, Fribergh and Sidoravicius \\cite{GAV2014} proved that speed of biased random walk $RW_\\lambda$ on a Galton-Watson tree without leaves is strictly decreasing for $\\lambda\\leq \\frac{m_1}{1160},$ where $m_1$ is minimal degree of the Galton-Watson tree. And A\\\"{\\i}d\\'{e}kon \\cite{EA2013} improved this result to $\\lambda\\leq \\frac{1}{2}.$ In this paper, we prove that for the $RW_{\\lambda}$ on a Galton-Watson tree without leaves, its speed is strictly decreasing for $\\lambda\\in \\left[0,\\frac{m_1}{1+\\sqrt{1-\\frac{1}{m_1}}}\\right]$ when $m_1\\geq 2;$ and we owe the proof to A\\\"{\\i}d\\'{e}kon \\cite{EA2013}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-10-26T02:37:10.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J15",
      "60J80"
    ],
    "keywords": [
      "biased random walk",
      "galton-watson tree",
      "monotonicity",
      "minimal degree",
      "sidoravicius"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}