{
  "id": "math/0604299",
  "version": "v1",
  "published": "2006-04-12T21:08:44.000Z",
  "updated": "2006-04-12T21:08:44.000Z",
  "title": "A note on subgaussian estimates for linear functionals on convex bodies",
  "authors": [
    "Apostolos Giannopoulos",
    "Alain Pajor",
    "Grigoris Paouris"
  ],
  "comment": "10 pages",
  "categories": [
    "math.FA",
    "math.MG"
  ],
  "abstract": "We give an alternative proof of a recent result of Klartag on the existence of almost subgaussian linear functionals on convex bodies. If $K$ is a convex body in ${\\mathbb R}^n$ with volume one and center of mass at the origin, there exists $x\\neq 0$ such that $$|\\{y\\in K: |< y,x> |\\gr t\\|<\\cdot, x>\\|_1\\}|\\ls\\exp (-ct^2/\\log^2(t+1))$$ for all $t\\gr 1$, where $c>0$ is an absolute constant. The proof is based on the study of the $L_q$--centroid bodies of $K$. Analogous results hold true for general log-concave measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2006-04-12T21:08:44.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "46B07",
      "52A20"
    ],
    "keywords": [
      "convex body",
      "subgaussian estimates",
      "analogous results hold true",
      "subgaussian linear functionals",
      "general log-concave measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 10,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2006math......4299G"
    }
  }
}