{
  "id": "2004.07562",
  "version": "v1",
  "published": "2020-04-16T10:00:21.000Z",
  "updated": "2020-04-16T10:00:21.000Z",
  "title": "Position Distribution of Run-and-Tumble particles in Two-dimensions",
  "authors": [
    "Ion Santra",
    "Urna Basu",
    "Sanjib Sabhapandit"
  ],
  "comment": "19 pages, 11 figures",
  "categories": [
    "cond-mat.stat-mech"
  ],
  "abstract": "We study a set of Run-and-tumble particle (RTP) dynamics in two spatial dimensions. In the first case of the orientation {\\theta} of the particle can assume a set of n possible discrete values while in the second case {\\theta} is a continuous variable. We calculate exactly the marginal position distributions for n = 3,4 and the continuous case and show that in all the cases the RTP shows a cross-over from a ballistic to diffusive regime. The ballistic regime is a typical signature of the active nature of the systems and is characterized by non-trivial position distributions which depends on the specific model. We also show that, the signature of activity at long-times can be found in the atypical fluctuations which we also characterize by computing the large deviation functions explicitly.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-04-16T10:00:21.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "run-and-tumble particle",
      "two-dimensions",
      "marginal position distributions",
      "non-trivial position distributions",
      "large deviation functions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 19,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}