{
  "id": "1410.0780",
  "version": "v1",
  "published": "2014-10-03T08:41:46.000Z",
  "updated": "2014-10-03T08:41:46.000Z",
  "title": "Small ball estimates for quasi-norms",
  "authors": [
    "Omer Friedland",
    "Ohad Giladi",
    "Olivier Guédon"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "This note contains two types of small ball estimates for random vectors in finite dimensional spaces equipped with a quasi-norm. In the first part, we obtain bounds for the small ball probability of random vectors under some smoothness assumptions on their density function. In the second part, we obtain Littlewood-Offord type estimates for quasi-norms. This generalizes a result which was previously obtained by Friedland and Sodin and by Rudelson and Vershynin.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-10-03T08:41:46.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "small ball estimates",
      "quasi-norm",
      "random vectors",
      "littlewood-offord type estimates",
      "small ball probability"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1410.0780F"
    }
  }
}