{
  "id": "1710.10679",
  "version": "v1",
  "published": "2017-10-29T19:46:44.000Z",
  "updated": "2017-10-29T19:46:44.000Z",
  "title": "Local limit theorems and mod-phi convergence",
  "authors": [
    "Martina dal Borgo",
    "Pierre-Loïc Méliot",
    "Ashkan Nikeghbali"
  ],
  "comment": "37 pages",
  "categories": [
    "math.PR"
  ],
  "abstract": "We prove local limit theorems for mod-{\\phi} convergent sequences of random variables, {\\phi} being a stable distribution. In particular, we give two new proofs of a local limit theorem in the framework of mod-phi convergence: one proof based on the notion of zone of control, and one proof based on the notion of mod-{\\phi} convergence in L1(iR). These new approaches allow us to identify the infinitesimal scales at which the stable approximation is valid. We complete our analysis with a large variety of examples to which our results apply, and which stem from random matrix theory, number theory, combinatorics or statistical mechanics.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2017-10-29T19:46:44.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "local limit theorem",
      "mod-phi convergence",
      "random matrix theory",
      "infinitesimal scales",
      "convergent sequences"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 37,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}