{
  "id": "1706.08342",
  "version": "v1",
  "published": "2017-06-26T12:39:59.000Z",
  "updated": "2017-06-26T12:39:59.000Z",
  "title": "Monotonicity of functionals of random polytopes",
  "authors": [
    "Mareen Beermann",
    "Matthias Reitzner"
  ],
  "categories": [
    "math.PR"
  ],
  "abstract": "The convex hull $P_{n}$ of a Gaussian sample $X_{1},...,X_{n}$ in $R^{d}$ is a Gaussian polytope. We prove that the expected number of facets $E f_{d-1} (P_n)$ is monotonically increasing in $n$. Furthermore we prove this for random polytopes generated by uniformly distributed points in a $d$-dimensional ball.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-06-26T12:39:59.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60D05"
    ],
    "keywords": [
      "random polytopes",
      "monotonicity",
      "functionals",
      "convex hull",
      "gaussian polytope"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}