{
  "id": "1905.13619",
  "version": "v1",
  "published": "2019-05-31T13:55:16.000Z",
  "updated": "2019-05-31T13:55:16.000Z",
  "title": "The cut metric for probability distributions",
  "authors": [
    "Amin Coja-Oghlan",
    "Max Hahn-Klimroth"
  ],
  "categories": [
    "math.CO",
    "cs.DM",
    "math-ph",
    "math.MP",
    "math.PR"
  ],
  "abstract": "Guided by the theory of graph limits, we investigate a variant of the cut metric for limit objects of sequences of discrete probability distributions. Apart from establishing basic results, we introduce a natural operation called {\\em pinning} on the space of limit objects and show how this operation yields a canonical cut metric approximation to a given probability distribution akin to the weak regularity lemma for graphons. We also establish the cut metric continuity of basic operations such as taking product measures.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-05-31T13:55:16.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60C05"
    ],
    "keywords": [
      "limit objects",
      "cut metric continuity",
      "discrete probability distributions",
      "weak regularity lemma",
      "probability distribution akin"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}