{
  "id": "1309.1348",
  "version": "v3",
  "published": "2013-09-05T13:50:32.000Z",
  "updated": "2015-09-06T06:22:28.000Z",
  "title": "Gaussian measures on the of space of Riemannian metrics",
  "authors": [
    "Brian Clarke",
    "Dmitry Jakobson",
    "Niky Kamran",
    "Lior Silberman",
    "Jonathan Taylor",
    "Yaiza Canzani"
  ],
  "comment": "16 pages; Final version submitted to journal per NSERC open access policy",
  "categories": [
    "math.DG",
    "math.PR"
  ],
  "abstract": "We introduce Gaussian-type measures on the manifold of all metrics with a fixed volume form on a compact Riemannian manifold of dimension $\\geq 3$. For this random model we compute the characteristic function for the $L^2$ (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics and give applications to the diameter, eigenvalue and volume entropy functionals.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2013-12-20T07:53:57.000Z",
      "title": "The manifold of metrics with a fixed volume form",
      "abstract": "We study the manifold of all metrics with the fixed volume form on a compact Riemannian manifold of dimension $\\geq 3$. We compute the characteristic function for the $L^2$ (Ebin) distance to the reference metric. In the Appendix, we study Lipschitz-type distance between Riemannian metrics, and give applications to the diameter and eigenvalue functionals.",
      "comment": "14 pages",
      "journal": null,
      "doi": null
    },
    {
      "version": "v3",
      "updated": "2015-09-06T06:22:28.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "57R25",
      "58B20",
      "58D17",
      "58D20",
      "58J50",
      "60G60",
      "53C21"
    ],
    "keywords": [
      "riemannian metrics",
      "gaussian measures",
      "compact riemannian manifold",
      "study lipschitz-type distance",
      "volume entropy functionals"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 16,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1309.1348C"
    }
  }
}