{
  "id": "0708.2152",
  "version": "v4",
  "published": "2007-08-16T08:14:32.000Z",
  "updated": "2015-06-29T08:18:12.000Z",
  "title": "Coupling, concentration inequalities and stochastic dynamics",
  "authors": [
    "Jean René Chazottes",
    "Pierre Collet",
    "Frank Redig"
  ],
  "comment": "33 pages, J. Math. Phys. 49 (2008). A typo in inequality (24) was corrected",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "In the context of interacting particle systems, we study the influence of the action of the semigroup on the concentration property of Lipschitz functions. As an application, this gives a new approach to estimate the relaxation speed to equilibrium of interacting particle systems. We illustrate our approach in a variety of examples for which we obtain several new results with short and non-technical proofs. These examples include the symmetric and asymmetric exclusion process and high-temperature spin-flip dynamics (\"Glauber dynamics\"). We also give a new proof of the Poincar\\'e inequality, based on coupling, in the context of one-dimensional Gibbs measures. In particular, we cover the case of polynomially decaying potentials, where the log-Sobolev inequality does not hold.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2008-09-05T09:36:38.000Z",
      "comment": "33 pages, one figure; minor corrections done; to appear in J. Math. Phys",
      "journal": null,
      "doi": null
    },
    {
      "version": "v4",
      "updated": "2015-06-29T08:18:12.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "82C22"
    ],
    "keywords": [
      "stochastic dynamics",
      "concentration inequalities",
      "interacting particle systems",
      "one-dimensional gibbs measures",
      "high-temperature spin-flip dynamics"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 33,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2007arXiv0708.2152R"
    }
  }
}