{
  "id": "1503.09190",
  "version": "v1",
  "published": "2015-03-31T19:59:12.000Z",
  "updated": "2015-03-31T19:59:12.000Z",
  "title": "Small ball probabilities, maximum density and rearrangements",
  "authors": [
    "T. Juškevičius",
    "J. D. Lee"
  ],
  "comment": "4 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the probability that a sum of independent random variables in $\\mathbb{R}^d$ with bounded densities lies in a ball is maximized by taking uniform distributions on spheres. This in turn generalizes a result by Rogozin on the maximum density of such sums on the line.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-03-31T19:59:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G50",
      "60F10",
      "60E05"
    ],
    "keywords": [
      "small ball probabilities",
      "maximum density",
      "probability",
      "rearrangements",
      "independent random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 4,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv150309190J"
    }
  }
}