{
  "id": "0903.0145",
  "version": "v5",
  "published": "2009-03-01T14:29:46.000Z",
  "updated": "2010-10-18T16:19:15.000Z",
  "title": "Limit Theorems for Optimal Mass Transportation",
  "authors": [
    "Gershon Wolansky"
  ],
  "categories": [
    "math.DS",
    "math.AP"
  ],
  "abstract": "The optimal mass transportation was introduced by Monge some 200 years ago and is, today, the source of large number of results in analysis, geometry and convexity. Here I investigate a new, surprising link between optimal transformations obtained by different Lagrangian actions on Riemannian manifolds. As a special case, for any pair of non-negative measures $\\lambda^+,\\lambda^-$ of equal mass $$ W_1(\\lambda^-, \\lambda^+)= \\lim_{\\eps\\to 0} \\eps^{-1}\\inf_{\\mu} W_p(\\mu+\\eps\\lambda^-, \\mu+\\eps\\lambda^+)$$ where $W_p$, $p\\geq 1$ is the Wasserstein distance and the infimum is over the set of probability measures in the ambient space.",
  "revisions": [
    {
      "version": "v5",
      "updated": "2010-10-18T16:19:15.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37K55",
      "70H20"
    ],
    "keywords": [
      "optimal mass transportation",
      "limit theorems",
      "ambient space",
      "large number",
      "lagrangian actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "2009arXiv0903.0145W"
    }
  }
}