{
  "id": "1605.08989",
  "version": "v1",
  "published": "2016-05-29T11:05:02.000Z",
  "updated": "2016-05-29T11:05:02.000Z",
  "title": "Partial orders on metric measure spaces",
  "authors": [
    "Max Grieshammer",
    "Thomas Rippl"
  ],
  "categories": [
    "math.PR",
    "math.MG"
  ],
  "abstract": "A partial order on the set of metric measure spaces is defined; it generalizes the Lipschitz order of Gromov. We show that our partial order is closed when metric measure spaces are equipped with the Gromov-weak topology and give a new characterization for the Lipschitz order. We will then consider some probabilistic applications. The main importance is given to the study of Fleming-Viot processes with different resampling rates. Besides that application we also consider tree-valued branching processes and two semigroups on metric measure spaces.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2016-05-29T11:05:02.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "metric measure spaces",
      "partial order",
      "lipschitz order",
      "gromov-weak topology",
      "probabilistic applications"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}