{
  "id": "1212.3004",
  "version": "v3",
  "published": "2012-12-12T22:13:36.000Z",
  "updated": "2015-02-09T01:35:06.000Z",
  "title": "The Speed of a Biased Walk on a Galton-Watson Tree without Leaves is Monotonic with Respect to Progeny Distributions for High Values of Bias",
  "authors": [
    "Behzad Mehrdad",
    "Sanchayan Sen",
    "Lingjiong Zhu"
  ],
  "comment": "20 pages",
  "journal": "Annales de l'Institut Henri Poincare-Probabilites et Statistiques 2015 Vol. 51, No. 1, 304-318",
  "categories": [
    "math.PR"
  ],
  "abstract": "Consider biased random walks on two Galton-Watson trees without leaves having progeny distributions $P_1$ and $P_2$ (GW$(P_1)$ and GW$(P_2)$) where $P_1$ and $P_2$ are supported on positive integers and $P_1$ dominates $P_2$ stochastically. We prove that the speed of the walk on GW$(P_1)$ is bigger than the same on GW$(P_2)$ when the bias is larger than a threshold depending on $P_1$ and $P_2$. This partially answers a question raised in \\citet*{BenArous}.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-06-23T21:08:07.000Z",
      "comment": "20 pages, to appear in Annales de l'Institut Henri Poincare",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-02-09T01:35:06.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60J80",
      "60G50"
    ],
    "keywords": [
      "galton-watson tree",
      "progeny distributions",
      "high values",
      "biased walk",
      "biased random walks"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 20,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015AnIHP..51..304M"
    }
  }
}