{
  "id": "2304.14551",
  "version": "v1",
  "published": "2023-04-27T22:12:24.000Z",
  "updated": "2023-04-27T22:12:24.000Z",
  "title": "The local limit theorem on nilpotent Lie groups",
  "authors": [
    "Timothée Bénard",
    "Emmanuel Breuillard"
  ],
  "comment": "56 pages. arXiv admin note: substantial text overlap with arXiv:2302.06024",
  "categories": [
    "math.PR",
    "math.DS"
  ],
  "abstract": "We establish the (non-lattice) local limit theorem for products of i.i.d. random variables on an arbitrary simply connected nilpotent Lie group $G$, where the variables are allowed to be non-centered. Our result also improves on the known centered case by proving uniformity for two-sided moderate deviations and allowing measures with a moment of order $2(\\dim G)^2$ without further regularity assumptions. As applications we establish a Ratner-type equidistribution theorem for unipotent walks on homogeneous spaces and obtain a new proof of the Choquet-Deny property in our setting.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2023-04-27T22:12:24.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "60B15",
      "60F05",
      "35H10",
      "35R03",
      "22E25",
      "58J65"
    ],
    "keywords": [
      "local limit theorem",
      "simply connected nilpotent lie group",
      "arbitrary simply connected nilpotent lie",
      "ratner-type equidistribution theorem",
      "random variables"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 56,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}