{
  "id": "2405.11845",
  "version": "v1",
  "published": "2024-05-20T07:38:51.000Z",
  "updated": "2024-05-20T07:38:51.000Z",
  "title": "Speed of Random Walks in Dirichlet Environment on a Galton-Watson Tree",
  "authors": [
    "Dongjian Qian",
    "Yang Xiao"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This paper deals with a transient random walk in Dirichlet environment, or equivalently a linearly edge reinforced random walk, on a Galton-Watson tree. We compute the stationary distribution of the environment seen from the particle of an edge reinforced random walk. We obtain a formula for the speed and give a necessary and sufficient condition for the walk to have a positive speed under some moment conditions on the offspring distribution of the tree.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-05-20T07:38:51.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K37",
      "60K35",
      "60J80",
      "60F15"
    ],
    "keywords": [
      "galton-watson tree",
      "dirichlet environment",
      "linearly edge reinforced random walk",
      "transient random walk",
      "moment conditions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}