{
  "id": "1109.4918",
  "version": "v1",
  "published": "2011-09-22T19:02:09.000Z",
  "updated": "2011-09-22T19:02:09.000Z",
  "title": "Tug-of-war and infinity Laplace equation with vanishing Neumann boundary condition",
  "authors": [
    "Tonći Antunović",
    "Yuval Peres",
    "Scott Sheffield",
    "Stephanie Somersille"
  ],
  "comment": "33 pages, 2 figures",
  "categories": [
    "math.AP",
    "math.PR"
  ],
  "abstract": "We study a version of the stochastic \"tug-of-war\" game, played on graphs and smooth domains, with the empty set of terminal states. We prove that, when the running payoff function is shifted by an appropriate constant, the values of the game after n steps converge in the continuous case and the case of finite graphs with loops. Using this we prove the existence of solutions to the infinity Laplace equation with vanishing Neumann boundary condition.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2011-09-22T19:02:09.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "35J70",
      "91A15",
      "91A24"
    ],
    "keywords": [
      "vanishing neumann boundary condition",
      "infinity laplace equation",
      "tug-of-war",
      "running payoff function",
      "smooth domains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2011arXiv1109.4918A"
    }
  }
}