{
  "id": "1412.4026",
  "version": "v1",
  "published": "2014-12-12T15:40:35.000Z",
  "updated": "2014-12-12T15:40:35.000Z",
  "title": "Asymptotic quantization for probability measures on Riemannian manifolds",
  "authors": [
    "Mikaela Iacobelli"
  ],
  "categories": [
    "math.AP"
  ],
  "abstract": "In this paper we study the quantization problem for probability measures on Riemannian manifolds. Under a suitable assumption on the growth at infinity of the measure we find asymptotic estimates for the quantization error, generalizing the results on $\\mathbb{R}^d.$ Our growth assumption depends on the curvature of the manifold and reduces, in the flat case, to a moment condition. We also build an example showing that our hypothesis is sharp.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2014-12-12T15:40:35.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "probability measures",
      "riemannian manifolds",
      "asymptotic quantization",
      "growth assumption depends",
      "asymptotic estimates"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2014arXiv1412.4026I"
    }
  }
}