{
  "id": "2201.01514",
  "version": "v2",
  "published": "2022-01-05T09:33:42.000Z",
  "updated": "2022-11-15T09:39:08.000Z",
  "title": "Local limit theorem for complex valued sequences",
  "authors": [
    "Lucas Coeuret"
  ],
  "categories": [
    "math.PR",
    "cs.NA",
    "math.NA"
  ],
  "abstract": "In this article, we study the pointwise asymptotic behavior of iterated convolutions on the one dimensional lattice Z. We generalize the so-called local limit theorem in probability theory to complex valued sequences. A sharp rate of convergence towards an explicitly computable attractor is proved together with a generalized Gaussian bound for the asymptotic expansion up to any order of the iterated convolution.",
  "revisions": [
    {
      "version": "v2",
      "updated": "2022-11-15T09:39:08.000Z"
    }
  ],
  "analyses": {
    "subjects": [
      "42A85",
      "35K25",
      "60F99",
      "65M12"
    ],
    "keywords": [
      "local limit theorem",
      "complex valued sequences",
      "iterated convolution",
      "asymptotic expansion",
      "pointwise asymptotic behavior"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}