{
  "id": "2103.06981",
  "version": "v1",
  "published": "2021-03-11T22:07:03.000Z",
  "updated": "2021-03-11T22:07:03.000Z",
  "title": "Should I stay or should I go? Zero-size jumps in random walks for Lévy flights",
  "authors": [
    "Gianni Pagnini",
    "Silvia Vitali"
  ],
  "journal": "Fract. Calc. Appl. Anal. 24(1), 137-167 (2021)",
  "doi": "10.1515/fca-2021-0007",
  "categories": [
    "cond-mat.stat-mech",
    "math.PR"
  ],
  "abstract": "We study Markovian continuous-time random walk models for L\\'evy flights and we show an example in which the convergence to stable densities is not guaranteed when jumps follow a bi-modal power-law distribution that is equal to zero in zero. The significance of this result is two-fold: i) with regard to the probabilistic derivation of the fractional diffusion equation and also ii) with regard to the concept of site fidelity in the framework of L\\'evy-like motion for wild animals.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-03-11T22:07:03.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J60",
      "60J25",
      "26A33",
      "60G52",
      "92D50"
    ],
    "keywords": [
      "lévy flights",
      "zero-size jumps",
      "markovian continuous-time random walk models",
      "study markovian continuous-time random walk",
      "bi-modal power-law distribution"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}