{
  "id": "1601.03957",
  "version": "v1",
  "published": "2016-01-15T15:15:26.000Z",
  "updated": "2016-01-15T15:15:26.000Z",
  "title": "Boundary of the range II: lower tails",
  "authors": [
    "Amine Asselah",
    "Bruno Schapira"
  ],
  "comment": "30p",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study downward deviations of the boundary of the range of a transient walk on the Euclidean lattice. We describe the optimal strategy adopted by the walk in order to shrink the boundary of its range. The technics we develop apply equally well to the range, and provide pathwise statements for the {\\it Swiss cheese} picture of Bolthausen, van den Berg and den Hollander \\cite{BBH}.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-01-15T15:15:26.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60G50"
    ],
    "keywords": [
      "lower tails",
      "van den berg",
      "euclidean lattice",
      "den hollander",
      "study downward deviations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2016arXiv160103957A"
    }
  }
}