{
  "id": "2012.02304",
  "version": "v1",
  "published": "2020-12-03T22:10:18.000Z",
  "updated": "2020-12-03T22:10:18.000Z",
  "title": "A characterization of transportation-information inequalities for Markov processes in terms of dimension-free concentration",
  "authors": [
    "Daniel Lacker",
    "Lane Chun Yeung"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Inequalities between transportation costs and Fisher information are known to characterize certain concentration properties of Markov processes around their invariant measures. This note provides a new characterization of the quadratic transportation-information inequality $W_2I$ in terms of a dimension-free concentration property for i.i.d. (conditionally on the initial positions) copies of the underlying Markov process. This parallels Gozlan's characterization of the quadratic transportation-entropy inequality $W_2H$. The proof is based on a new Laplace-type principle for the operator norms of Feynman-Kac semigroups, which is of independent interest. Lastly, we illustrate how both our theorem and (a form of) Gozlan's are instances of a general convex-analytic tensorization principle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-12-03T22:10:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "markov process",
      "general convex-analytic tensorization principle",
      "quadratic transportation-entropy inequality",
      "dimension-free concentration property",
      "parallels gozlans characterization"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}