{
  "id": "1511.06250",
  "version": "v1",
  "published": "2015-11-19T16:47:40.000Z",
  "updated": "2015-11-19T16:47:40.000Z",
  "title": "Discrete Bochner inequalities via the Bochner-Bakry-Emery approach for Markov chains",
  "authors": [
    "Ansgar Jüngel",
    "Wen Yue"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Discrete Beckner inequalities, which interpolate between the modified logarithmic Sobolev inequality and the Poincar\\'e inequality, are derived for time-continuous Markov chains on countable state spaces. The proof is based on the Bakry-Emery approach and on discrete Bochner-type inequalities established by Caputo, Dai Pra, and Posta and recently extended by Fathi and Maas. The abstract result is applied to several Markov chains, including birth-death processes, zero-range processes, Bernoulli-Laplace models, and random transportation models, and to a finite-volume discretization of a one-dimensional Fokker-Planck equation, applying results by Mielke.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2015-11-19T16:47:40.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60J27",
      "39B62",
      "60J80"
    ],
    "keywords": [
      "discrete bochner inequalities",
      "markov chains",
      "bochner-bakry-emery approach",
      "discrete beckner inequalities",
      "one-dimensional fokker-planck equation"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2015arXiv151106250J"
    }
  }
}