{
  "id": "math/0405341",
  "version": "v2",
  "published": "2004-05-18T02:05:07.000Z",
  "updated": "2021-04-11T19:40:34.000Z",
  "title": "A note on Talagrand's concentration inequality for empirical processes",
  "authors": [
    "Dmitry Panchenko"
  ],
  "journal": "2001 Elect. Comm. in Probab. 6, 55-65",
  "categories": [
    "math.PR"
  ],
  "abstract": "In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different shorter proof of the main technical lemma that guarantees the existence of a certain kernel. Our proof provides the almost optimal value of the constant involved in the statement of this lemma.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-05-18T02:05:07.000Z",
      "abstract": "In this paper we revisit Talagrand's proof of concentration inequality for empirical processes. We give a different shorter proof of the main technical lemma that garantees the existence of a certain kernel. Our proof provides the almost optimal value of the constant involved in the statement of this lemma.",
      "comment": "7 pages",
      "doi": null
    },
    {
      "version": "v2",
      "updated": "2021-04-11T19:40:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G20"
    ],
    "keywords": [
      "talagrands concentration inequality",
      "empirical processes",
      "revisit talagrands proof",
      "optimal value",
      "main technical lemma"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 7,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......5341P"
    }
  }
}