{
  "id": "1909.13274",
  "version": "v1",
  "published": "2019-09-29T13:04:34.000Z",
  "updated": "2019-09-29T13:04:34.000Z",
  "title": "Asymptotic results for stabilizing functionals of point processes having fast decay of correlations",
  "authors": [
    "Marcel Fenzl"
  ],
  "comment": "38 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We establish precise bounds on cumulants for a rather general class of non-linear geometric functionals satisfying the stabilization property under a simple, stationary (marked) point process admitting fast decay of its correlation functions and thereby conclude a Berry-Esseen bound, a concentration inequality, a moderate deviation principle and a Marcinkiewicz-Zygmund-type strong law of large numbers. The result is applied to the germ-grain model as well as to random sequential absorption for ${\\alpha}$-determinantal point processes having fast decaying kernels and certain Gibbsian point processes. The proof relies on cumulant expansions using a clustering result as well as factorial moment expansions for point processes.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-09-29T13:04:34.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60F10",
      "60D05",
      "60G55",
      "05C80",
      "52A22"
    ],
    "keywords": [
      "asymptotic results",
      "stabilizing functionals",
      "correlation",
      "point process admitting fast decay",
      "marcinkiewicz-zygmund-type strong law"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 38,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}