{
  "id": "math/0406364",
  "version": "v1",
  "published": "2004-06-18T17:55:37.000Z",
  "updated": "2004-06-18T17:55:37.000Z",
  "title": "A Thinning Analogue of de Finetti's Theorem",
  "authors": [
    "Shannon Starr"
  ],
  "comment": "30 pages, 1 figure",
  "categories": [
    "math.PR",
    "math-ph",
    "math.MP"
  ],
  "abstract": "We consider a notion of uniform thinning for a finite sequence of random variables $(X_1,...,X_n)$ obtained by removing one random variable, uniformly at random. If a triangular array of random variables $(X_{n,k} : n \\in \\mathbb{N}_+, 1 \\le k \\le n)$ satisfies that the law of $(X_{n,1},...,X_{n,n})$ is obtained by uniformly thinning $(X_{n+1,1},...,X_{n+1,n+1})$, then we call the array thinning-invariant. We give a representation for the Choquet simplex of all thinning-invariant triangular arrays of random variables, when all random variables take values in a compact metric space (with Borel measurable distributions). We give two applications: to long-ranged, asymmetric classical spin chains, and long-ranged, asymmetric simple exclusion processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2004-06-18T17:55:37.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G09",
      "82B20",
      "60J10"
    ],
    "keywords": [
      "finettis theorem",
      "random variable",
      "thinning analogue",
      "asymmetric simple exclusion processes",
      "asymmetric classical spin chains"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 30,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2004math......6364S"
    }
  }
}