{
  "id": "1209.3098",
  "version": "v3",
  "published": "2012-09-14T06:08:46.000Z",
  "updated": "2013-06-18T16:54:25.000Z",
  "title": "Portmanteau inequalities on the Poisson space: mixed regimes and multidimensional clustering",
  "authors": [
    "Solesne Bourguin",
    "Giovanni Peccati"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "Using Malliavin operators together with an interpolation technique inspired by Arratia, Goldstein and Gordon (1989), we prove a new inequality on the Poisson space, allowing one to measure the distance between the laws of a general random vector, and of a target random element composed of Gaussian and Poisson random variables. Several consequences are deduced from this result, in particular: (1) new abstract criteria for multidimensional stable convergence on the Poisson space, (2) a class of mixed limit theorems, involving both Poisson and Gaussian limits, (3) criteria for the asymptotic independence of $U$-statistics obeying to Gaussian and Poisson asymptotic regimes. Our results generalize and unify several previous findings in the field. We provide an application to joint sub-graph counting in random geometric graphs.",
  "revisions": [
    {
      "version": "v3",
      "updated": "2013-06-18T16:54:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "poisson space",
      "portmanteau inequalities",
      "mixed regimes",
      "multidimensional clustering",
      "inequality"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2012arXiv1209.3098B"
    }
  }
}