{
  "id": "1702.04698",
  "version": "v1",
  "published": "2017-02-15T18:06:28.000Z",
  "updated": "2017-02-15T18:06:28.000Z",
  "title": "A characterization of a class of convex log-Sobolev inequalities on the real line",
  "authors": [
    "Yan Shu",
    "Michał Strzelecki"
  ],
  "comment": "17 pages",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We give a sufficient and necessary condition for a probability measure $\\mu$ on the real line to satisfy the logarithmic Sobolev inequality for convex functions. The condition is expressed in terms of the unique left-continuous and non-decreasing map transporting the symmetric exponential measure onto $\\mu$. The main tool in the proof is the theory of weak transport costs. As a consequence, we obtain dimension-free concentration bounds for the lower and upper tails of convex functions of independent random variables which satisfy the convex log-Sobolev inequality.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-02-15T18:06:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60E15",
      "26A51",
      "26D10"
    ],
    "keywords": [
      "convex log-sobolev inequality",
      "real line",
      "convex functions",
      "characterization",
      "logarithmic sobolev inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}