{
  "id": "2412.20315",
  "version": "v1",
  "published": "2024-12-29T01:39:16.000Z",
  "updated": "2024-12-29T01:39:16.000Z",
  "title": "On the joint distribution of the area and the number of peaks for Bernoulli excursions",
  "authors": [
    "Vladislav Kargin"
  ],
  "comment": "21 pages, 1 figure",
  "journal": "Bernoulli 30(4), 2024, 2700--2720",
  "doi": "10.3150/23-BEJ1691",
  "categories": [
    "math.PR",
    "math.CO"
  ],
  "abstract": "Let $P_n$ be a random Bernoulli excursion of length $2n$. We show that the area under $P_n$ and the number of peaks of $P_n$ are asymptotically independent. We also show that these statistics have the correlation coefficient asymptotic to $c /\\sqrt{n}$ for large $n$, where $c < 0$, and explicitly compute the coefficient $c$.",
  "revisions": [
    {
      "version": "v1",
      "updated": "2024-12-29T01:39:16.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "joint distribution",
      "random bernoulli excursion",
      "correlation coefficient asymptotic",
      "statistics",
      "asymptotically independent"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 21,
      "language": "en",
      "license": "arXiv",
      "status": "editable"
    }
  }
}