{
  "id": "2208.06330",
  "version": "v1",
  "published": "2022-08-12T15:38:19.000Z",
  "updated": "2022-08-12T15:38:19.000Z",
  "title": "A universal lower bound for the discrepancies of actions of a locally compact group",
  "authors": [
    "Antoine Pinochet Lobos",
    "Christophe Pittet"
  ],
  "comment": "17 pages, 1 figure",
  "categories": [
    "math.DS"
  ],
  "abstract": "We prove a universal lower bound for the discrepancies of measure-preserving actions of a locally compact group on an atomless probability space. It generalizes the universal lower bound for the discrepancies of measure-preserving actions of a discrete group. Many examples show that the generalization from discrete groups to locally compact groups requires some additional hypothesis on the action (we detail some examples due to Margulis). Well-known examples and results of Kazdhan and Zimmer show that the discrepancies of some actions of Lie groups on homogeneous spaces match exactly the universal lower bounds we prove.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2022-08-12T15:38:19.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "37A15",
      "37A30"
    ],
    "keywords": [
      "universal lower bound",
      "locally compact group",
      "discrepancies",
      "discrete group",
      "measure-preserving actions"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 17,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}