{
  "id": "1703.04971",
  "version": "v1",
  "published": "2017-03-15T07:01:45.000Z",
  "updated": "2017-03-15T07:01:45.000Z",
  "title": "Concentration inequalities for measures of a Boolean model",
  "authors": [
    "Günter Last",
    "Fabian Gieringer"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "We consider a Boolean model $Z$ driven by a Poisson particle process $\\eta$ on a metric space $\\mathbb{Y}$. We study the random variable $\\rho(Z)$, where $\\rho$ is a (deterministic) measure on $\\mathbb{Y}$. Due to the interaction of overlapping particles, the distribution of $\\rho(Z)$ cannot be described explicitly. In this note we derive concentration inequalities for $\\rho(Z)$. To this end we first prove two concentration inequalities for functions of a Poisson process on a general phase space.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-03-15T07:01:45.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05",
      "60G55"
    ],
    "keywords": [
      "boolean model",
      "general phase space",
      "poisson particle process",
      "metric space",
      "poisson process"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}