{
  "id": "math/0209278",
  "version": "v2",
  "published": "2002-09-20T21:28:44.000Z",
  "updated": "2002-10-02T21:06:58.000Z",
  "title": "The optimal order for the p-th moment of sums of independent random variables with respect to symmetric norms and related combinatorial estimates",
  "authors": [
    "Marius Junge"
  ],
  "categories": [
    "math.PR",
    "math.OA"
  ],
  "abstract": "We calculate the p-the moment of the sum of n independent random variables with respect to symmetric norm in R^n. The order of growth for upper bound p/ln p obtained in ths estimate is optimal. The result extends to generalized Lorentz spaces l_{f,w} under mild assumptions on f. Indeed, the key combinatorial estimate is obtained for the weak l_1 (l_{1,infinity})-norm. Similar results have been obtained independently by Gordon, Litvak, Schuett and Werner for Orlicz norms and by Montgomery-Smith using different techniques and avoiding the combinatorial estimate.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2002-10-02T21:06:58.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B09",
      "60G50",
      "60C05",
      "47L20"
    ],
    "keywords": [
      "independent random variables",
      "related combinatorial estimates",
      "symmetric norm",
      "p-th moment",
      "optimal order"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2002math......9278J"
    }
  }
}