{
  "id": "0902.0743",
  "version": "v2",
  "published": "2009-02-04T16:43:06.000Z",
  "updated": "2009-02-27T10:07:55.000Z",
  "title": "Isoperimetry for spherically symmetric log-concave probability measures",
  "authors": [
    "Nolwen Huet"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove an isoperimetric inequality for probability measures $\\mu$ on $\\mathbb{R}^n$ with density proportional to $\\exp(-\\phi(\\lambda | x|))$, where $|x|$ is the euclidean norm on $\\mathbb{R}^n$ and $\\phi$ is a non-decreasing convex function. It applies in particular when $\\phi(x)=x^\\alpha$ with $\\alpha\\ge1$. Under mild assumptions on $\\phi$, the inequality is dimension-free if $\\lambda$ is chosen such that the covariance of $\\mu$ is the identity.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2009-02-27T10:07:55.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "26D10",
      "60E15",
      "28A75"
    ],
    "keywords": [
      "spherically symmetric log-concave probability measures",
      "isoperimetry",
      "isoperimetric inequality",
      "density proportional",
      "euclidean norm"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0902.0743H"
    }
  }
}