{
  "id": "1612.05983",
  "version": "v1",
  "published": "2016-12-18T20:25:25.000Z",
  "updated": "2016-12-18T20:25:25.000Z",
  "title": "Nonexistence of fractional Brownian fields indexed by cylinders",
  "authors": [
    "Nil Venet"
  ],
  "comment": "23 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We show in this paper that there exists no $H$-fractional Brownian field indexed by the cylinder $\\mathbb{S}^1 \\times ]0,\\varepsilon[$ endowed with its product distance for any $\\varepsilon>0$ and $H>0$. As a consequence we show that the fractional index of a compact metric space is not continuous with respect to the Gromov-Hausdorff convergence. The result holds for Riemannian products with a minimal closed geodesic. We also investigate the case of the cylinder endowed with a distance asymptotically close to the product distance in the neighbourhood of a circle.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-12-18T20:25:25.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "fractional brownian field",
      "product distance",
      "nonexistence",
      "compact metric space",
      "distance asymptotically close"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 23,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}