{
  "id": "1004.3482",
  "version": "v4",
  "published": "2010-04-20T15:36:57.000Z",
  "updated": "2010-10-01T13:11:06.000Z",
  "title": "Concentration inequalities for Gibbs measures",
  "authors": [
    "Ioannis Papageorgiou"
  ],
  "comment": "28 pages, accepted for publication at Infinite Dimensional Analysis, Quantum Probability and Related Topics",
  "categories": [
    "math.PR",
    "math.FA"
  ],
  "abstract": "We are interested in Sobolev type inequalities and their relationship with concentration properties on higher dimensions. We consider unbounded spin systems on the d-dimensional lattice with interactions that increase slower than a quadratic. At first we assume that the one site measure satisfies a Modified log-Sobolev inequality with a constant uniformly on the boundary conditions and we determine conditions so that the infinite dimensional Gibbs measure satisfies a concentration as well as a Talagrand type inequality. Then a Modified Log-Sobolev type concentration property is obtained under weaker conditions referring to the Log-Sobolev inequalities for the boundary free measure.",
  "revisions": [
    {
      "version": "v4",
      "updated": "2010-10-01T13:11:06.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "concentration inequalities",
      "infinite dimensional gibbs measure satisfies",
      "modified log-sobolev type concentration property",
      "log-sobolev inequality",
      "talagrand type inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 28,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2010arXiv1004.3482P"
    }
  }
}