{
  "id": "2406.08370",
  "version": "v1",
  "published": "2024-06-12T16:18:26.000Z",
  "updated": "2024-06-12T16:18:26.000Z",
  "title": "A law of the iterated logarithm for the number of blocks in regenerative compositions generated by gamma-like subordinators",
  "authors": [
    "Alexander Iksanov",
    "Wissem Jedidi"
  ],
  "comment": "15 pages, submitted for publication",
  "categories": [
    "math.PR"
  ],
  "abstract": "The points of the closed range of a drift-free subordinator with no killing are used for separating into blocks the elements of a sample of size $n$ from the standard exponential distribution. This gives rise to a random composition of $n$. Assuming that the subordinator has the L\\'{e}vy measure, which behaves near zero like the gamma subordinator, we prove a law of the iterated logarithm for the number of blocks in the composition as $n$ tends to infinity. Along the way we prove a law of the iterated logarithm for the Lebesgue convolution of a standard Brownian motion and a deterministic regularly varying function. This result may be of independent interest.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-06-12T16:18:26.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "iterated logarithm",
      "regenerative compositions",
      "gamma-like subordinators",
      "standard exponential distribution",
      "standard brownian motion"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 15,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}