{
  "id": "1503.06948",
  "version": "v1",
  "published": "2015-03-24T08:40:57.000Z",
  "updated": "2015-03-24T08:40:57.000Z",
  "title": "Convergence of discrete Green functions with Neumann boundary conditions",
  "authors": [
    "Shirshendu Ganguly",
    "Yuval Peres"
  ],
  "comment": "23 pages, 6 figures",
  "categories": [
    "math.PR",
    "cond-mat.stat-mech",
    "math.AP",
    "math.CV"
  ],
  "abstract": "In this note we prove convergence of Green functions with Neumann boundary conditions for the random walk to their continuous counterparts. Also a few Beurling type hitting estimates are obtained. These have been used recently in the study of a two dimensional competing aggregation system known as $Competitive\\, Erosion$. Some of the statements appearing in this note are classical for ${\\mathbb{Z}}^2$. However additional arguments are needed for the proofs in the bounded geometry setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-24T08:40:57.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "neumann boundary conditions",
      "discrete green functions",
      "convergence",
      "dimensional competing aggregation system",
      "additional arguments"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150306948G"
    }
  }
}