{
  "id": "1309.6459",
  "version": "v1",
  "published": "2013-09-25T10:57:23.000Z",
  "updated": "2013-09-25T10:57:23.000Z",
  "title": "Probability Law For the Euclidean Distance Between Two Planar Random Flights",
  "authors": [
    "Alexander D. Kolesink"
  ],
  "comment": "27 pages",
  "journal": "Journal of Statistical Physics, 2014, vol.154, pp.1124-1152",
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider two independent symmetric Markov random flights $\\bold Z_1(t)$ and $\\bold Z_2(t)$ performed by the particles that simultaneously start from the origin of the Euclidean plane $\\Bbb R^2$ in random directions distributed uniformly on the unit circumference $S_1$ and move with constant finite velocities $c_1>0, \\; c_2>0$, respectively. The new random directions are taking uniformly on $S_1$ at random time instants that form independent homogeneous Poisson flows of rates $\\lambda_1>0, \\; \\lambda_2>0$. The probability distribution function of the Euclidean distance $$\\rho(t)=\\Vert \\bold Z_1(t) - \\bold Z_2(t) \\Vert, \\qquad t>0,$$ between $\\bold Z_1(t)$ and $\\bold Z_2(t)$ at arbitrary time instant $t>0$, is obtained.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-09-25T10:57:23.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60J60",
      "60J65",
      "82C41",
      "82C70"
    ],
    "keywords": [
      "planar random flights",
      "euclidean distance",
      "probability law",
      "independent symmetric markov random flights",
      "time instant"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 27,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.6459K"
    }
  }
}