{
  "id": "2009.03609",
  "version": "v1",
  "published": "2020-09-08T09:40:50.000Z",
  "updated": "2020-09-08T09:40:50.000Z",
  "title": "Random walks on generalized visible lattice points",
  "authors": [
    "Kui Liu",
    "Xianchang Meng"
  ],
  "comment": "17 pages, comments are welcome",
  "categories": [
    "math.NT",
    "math.CO",
    "math.PR"
  ],
  "abstract": "We consider the proportion of generalized visible lattice points in the plane visited by random walkers. Our work concerns the visible lattice points in random walks in three aspects: (1) generalized visibility along curves; (2) one random walker visible from multiple watchpoints; (3) simultaneous visibility of multiple random walkers. Moreover, we found new phenomenon in the case of multiple random walkers: for visibility along a large class of curves and for any number of random walkers, the proportion of steps at which all random walkers are visible simultaneously is almost surely larger than a positive constant.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-09-08T09:40:50.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "11H06",
      "11N37"
    ],
    "keywords": [
      "generalized visible lattice points",
      "random walks",
      "multiple random walkers",
      "visibility",
      "large class"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}