{
  "id": "2108.06303",
  "version": "v1",
  "published": "2021-08-13T16:17:56.000Z",
  "updated": "2021-08-13T16:17:56.000Z",
  "title": "On the uniqueness of Gibbs distributions with a non-negative and subcritical pair potential",
  "authors": [
    "Steffen Betsch",
    "Günter Last"
  ],
  "comment": "23 pages, 5 tables",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove that the distribution of a Gibbs process with non-negative pair potential is uniquely determined as soon as an associated Poisson-driven random connection model (RCM) does not percolate. Our proof combines disagreement coupling in continuum with a coupling of a Gibbs process and a RCM. The improvement over previous uniqueness results is illustrated both in theory and simulations.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2021-08-13T16:17:56.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60K35",
      "60G55",
      "60D05"
    ],
    "keywords": [
      "subcritical pair potential",
      "gibbs distributions",
      "associated poisson-driven random connection model",
      "gibbs process",
      "uniqueness results"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}