{
  "id": "1606.00988",
  "version": "v1",
  "published": "2016-06-03T07:24:19.000Z",
  "updated": "2016-06-03T07:24:19.000Z",
  "title": "Time averages in continuous time random walks",
  "authors": [
    "Felix Thiel",
    "Igor M. Sokolov"
  ],
  "comment": "5 pages",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We investigate the time averaged squared displacement (TASD) of continuous time random walks with respect to the number of steps $N$, which the random walker performed during the data acquisition time $T$. We prove that the TASD, and as well the apparent diffusion constant, grow linearly with $N$, provided the steps possess a fourth moment and can not accumulate in small intervals. Consequently, the fluctuations of the latter are dominated by the fluctuations of $N$, and fluctuations of the walker's thermal history are irrelevant. Furthermore, we show that the relative scatter decays as $1/\\sqrt{N}$, which suppresses all non-linear features in a plot of the TASD against the lag time. Parts of our arguments also hold for continuous time random walks with correlated steps.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-06-03T07:24:19.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "continuous time random walks",
      "time averages",
      "fluctuations",
      "data acquisition time",
      "apparent diffusion constant"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 5,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}