{
  "id": "1911.09563",
  "version": "v1",
  "published": "2019-11-21T15:57:34.000Z",
  "updated": "2019-11-21T15:57:34.000Z",
  "title": "Monotonicity of escape probabilities for branching random walks on $\\Z^{d}$",
  "authors": [
    "Achillefs Tzioufas"
  ],
  "comment": "13pp",
  "categories": [
    "math.PR"
  ],
  "abstract": "We study nearest-neighbors branching random walks started by a single particle at the interior of a hypercube. We show that the probability of its progeny escaping a hypercube is monotonically decreasing with respect to the distance of the starting point from the boundary of the hypercube. We derive as a consequence that at all times the number of particles at a site is monotonically decreasing with respect to its distance from the starting site.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-21T15:57:34.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "escape probabilities",
      "probability",
      "study nearest-neighbors branching random walks",
      "monotonicity",
      "single particle"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 13,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}