{
  "id": "1612.05984",
  "version": "v1",
  "published": "2016-12-18T20:28:18.000Z",
  "updated": "2016-12-18T20:28:18.000Z",
  "title": "On the existence of fractional Brownian fields indexed by manifolds with closed geodesics",
  "authors": [
    "Nil Venet"
  ],
  "comment": "26 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We give a necessary condition of geometric nature for the existence of the $H$-fractional Brownian field indexed by a Riemannian manifold. In the case of the L\\'evy Brownian field ($H=1/2$) indexed by manifolds with minimising closed geodesics it turns out to be very strong. In particular we show that compact manifolds admitting a L\\'evy Brownian field are simply connected. We also derive from our result the non-degenerescence of the L\\'evy Brownian field indexed by hyperbolic spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-18T20:28:18.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional brownian field",
      "levy brownian field",
      "compact manifolds",
      "riemannian manifold",
      "geometric nature"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 26,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}