{
  "id": "1911.08100",
  "version": "v1",
  "published": "2019-11-19T05:08:07.000Z",
  "updated": "2019-11-19T05:08:07.000Z",
  "title": "On critical points of Gaussian random fields under diffeomorphic transformations",
  "authors": [
    "Dan Cheng",
    "Armin Schwartzman"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let $\\{X(t), t\\in M\\}$ and $\\{Z(t'), t'\\in M'\\}$ be smooth Gaussian random fields parameterized on Riemannian manifolds $M$ and $M'$, respectively, such that $X(t) = Z(f(t))$, where $f: M \\to M'$ is a diffeomorphic transformation. We study the expected number and height distribution of the critical points of $X$ in connection with those of $Z$. As an important case, when $X$ is an anisotropic Gaussian random field, then we show that its expected number of critical points becomes proportional to that of an isotropic field $Z$, while the height distribution remains the same as that of $Z$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2019-11-19T05:08:07.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60G15",
      "60G60",
      "15B52"
    ],
    "keywords": [
      "critical points",
      "diffeomorphic transformation",
      "anisotropic gaussian random field",
      "smooth gaussian random fields",
      "expected number"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}