{
  "id": "1312.2128",
  "version": "v1",
  "published": "2013-12-07T19:12:00.000Z",
  "updated": "2013-12-07T19:12:00.000Z",
  "title": "On the rate of convergence in Wasserstein distance of the empirical measure",
  "authors": [
    "Nicolas Fournier",
    "Arnaud Guillin"
  ],
  "categories": [
    "math.PR",
    "math.ST",
    "stat.TH"
  ],
  "abstract": "Let $\\mu_N$ be the empirical measure associated to a $N$-sample of a given probability distribution $\\mu$ on $\\mathbb{R}^d$. We are interested in the rate of convergence of $\\mu_N$ to $\\mu$, when measured in the Wasserstein distance of order $p>0$. We provide some satisfying non-asymptotic $L^p$-bounds and concentration inequalities, for any values of $p>0$ and $d\\geq 1$. We extend also the non asymptotic $L^p$-bounds to stationary $\\rho$-mixing sequences, Markov chains, and to some interacting particle systems.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2013-12-07T19:12:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "wasserstein distance",
      "empirical measure",
      "convergence",
      "interacting particle systems",
      "probability distribution"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2013arXiv1312.2128F"
    }
  }
}