{
  "abstract": "Let $f$ be a Rademacher random multiplicative function supported on the squarefree integers. We investigate the almost sure fluctuations of the restricted sum $M^{>}(x)=\\sum_{n\\le x;~ P(n)>x^{1/2}}f(n)$, where $P(n)$ is the largest prime factor of $n$. With $Q(x)$ being the conditional variance of $M^{>}(x)$ given the values of $f$ at primes not exceeding $x^{1/2}$, we prove that, almost surely, the upper and lower limits of $M^{>}(x)(2Q(x)\\log\\log Q(x))^{-1/2}$ as $x\\to\\infty$ are $1$ and $-1$, respectively. Furthermore, it is shown that the almost sure cluster set of the normalized sum is $[-1,1]$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.40707",
  "author_total": 2,
  "authors": [
    {
      "name": "Dariusz Buraczewski"
    },
    {
      "name": "Alexander Iksanov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2f34wy56y6x4a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.40707",
  "fulltext_url": null,
  "id": "2f34wy56y6x4a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.40707",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.NT"
    ],
    [
      "arxiv",
      "math.PR"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2610.40707",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2f34wy56y6x4a.ris",
  "sources": [
    {
      "first_seen": "2026-11-02T12:21:20Z",
      "native_id": "2610.40707",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.40707"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.NT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A law of the iterated logarithm for random multiplicative functions on integers with a large prime factor",
  "title_text": "A law of the iterated logarithm for random multiplicative functions on integers with a large prime factor",
  "type": "preprint",
  "updated_at": "2026-11-04T15:20:52Z",
  "url": "https://research.draconitic.com/paper/2f34wy56y6x4a",
  "venue": "arXiv",
  "versions": []
}