{
  "id": "2006.05320",
  "version": "v1",
  "published": "2020-06-09T14:55:12.000Z",
  "updated": "2020-06-09T14:55:12.000Z",
  "title": "Gaussian concentration and uniqueness of equilibrium states in lattice systems",
  "authors": [
    "J. -R. Chazottes",
    "J. Moles",
    "F. Redig",
    "E. Ugalde"
  ],
  "comment": "23 pages. Preprint",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider equilibrium states (that is, shift-invariant Gibbs measures) on the configuration space $S^{\\mathbb{Z}^d}$ where $d\\geq 1$ and $S$ is a finite set. We prove that if an equilibrium state for a shift-invariant uniformly summable potential satisfies a Gaussian concentration bound, then it is unique. Equivalently, if there exist several equilibrium states for a potential, none of them can satisfy such a bound.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2020-06-09T14:55:12.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "equilibrium state",
      "lattice systems",
      "uniqueness",
      "shift-invariant gibbs measures",
      "shift-invariant uniformly summable potential satisfies"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}