{
  "id": "1707.03725",
  "version": "v1",
  "published": "2017-07-12T14:02:36.000Z",
  "updated": "2017-07-12T14:02:36.000Z",
  "title": "On the expected diameter of planar Brownian motion",
  "authors": [
    "James McRedmond",
    "Chang Xu"
  ],
  "comment": "5 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "Known results show that the diameter $d_1$ of the trace of planar Brownian motion run for unit time satisfies $1.595 \\leq \\mathbb{E} d_1 \\leq 2.507$. This note improves these bounds to $1.601 \\leq \\mathbb{E} d_1 \\leq 2.355$. Simulations suggest that $\\mathbb{E} d_1 \\approx 1.99$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-07-12T14:02:36.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J65",
      "60D05"
    ],
    "keywords": [
      "expected diameter",
      "planar brownian motion run",
      "unit time satisfies",
      "simulations"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}