{
  "id": "1411.5982",
  "version": "v1",
  "published": "2014-11-21T19:15:05.000Z",
  "updated": "2014-11-21T19:15:05.000Z",
  "title": "A note on spectral gap and weighted Poincaré inequalities for some one-dimensional diffusions",
  "authors": [
    "Michel Bonnefont",
    "Aldéric Joulin",
    "Yutao Ma"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We present some classical and weighted Poincar\\'e inequalities for some one-dimensional probability measures. This work is the one-dimensional counterpart of a recent study achieved by the authors for a class of spherically symmetric probability measures in dimension larger than 2. Our strategy is based on two main ingredients: on the one hand, the optimal constant in the desired weighted Poincar\\'e inequality has to be rewritten as the spectral gap of a convenient Markovian diffusion operator, and on the other hand we use a recent result given by the two first authors, which allows to estimate precisely this spectral gap. In particular we are able to capture its exact value for some examples.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-11-21T19:15:05.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "spectral gap",
      "one-dimensional diffusions",
      "weighted poincare inequality",
      "convenient markovian diffusion operator",
      "one-dimensional probability measures"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1411.5982B"
    }
  }
}