{
  "id": "2008.08858",
  "version": "v1",
  "published": "2020-08-20T09:38:46.000Z",
  "updated": "2020-08-20T09:38:46.000Z",
  "title": "On a class of random sets of positive integers",
  "authors": [
    "Yong Han",
    "Yanqi Qiu",
    "Zipeng Wang"
  ],
  "comment": "9 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this note, we study a class of random subsets of positive integers induced by Bernoulli random variables. We obtain sufficient conditions such that the random set is almost surely lacunary, does not have bounded gaps and contains infinitely many arithmetic progressions, respectively.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-08-20T09:38:46.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G55",
      "60C05"
    ],
    "keywords": [
      "random set",
      "positive integers",
      "bernoulli random variables",
      "sufficient conditions",
      "random subsets"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 9,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}