{
  "abstract": "At Hermite rank two, the constant in the weighted law of the iterated logarithm under long-range dependence is represented as the largest eigenvalue of a suitably normalized positive integral operator on the unit interval. The same eigenvalue determines the exponential-moment threshold and the logarithmic right-tail rate of the weighted second-chaos limit, which in the unweighted case is the Rosenblatt law. The weighted third spectral moment is evaluated in closed form. Convergent two-sided spectral enclosures are obtained, and in the weight-concentration limit the leading eigenvalue is characterized by a scalar equation with a uniform geometric remainder. At the unweighted memory boundary, the constant decays like the square root of the distance to criticality. Its leading coefficient is determined to $25$ decimal places with certified full-operator residual bounds. After division by the square-root boundary factor, the weight-concentration and memory limits commute. Their common coefficient differs from the unweighted boundary coefficient and lies in the certified interval $(1.370323114331,\\,1.370323114332)$. The joint asymptotic formula is established with a uniform two-parameter remainder bound.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.30331",
  "author_total": 1,
  "authors": [
    {
      "name": "Elina Moldavskaya"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8634grvhkmhvq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.30331",
  "fulltext_url": null,
  "id": "8634grvhkmhvq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.30331",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7214609988",
  "pdf_url": "https://arxiv.org/pdf/2609.30331",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8634grvhkmhvq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:24:57Z",
      "native_id": "2609.30331",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.30331"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Constants in the Weighted Law of the Iterated Logarithm under Long-Range Dependence: Hermite Rank Two",
  "title_text": "Constants in the Weighted Law of the Iterated Logarithm under Long-Range Dependence: Hermite Rank Two",
  "type": "preprint",
  "updated_at": "2026-10-30T12:24:57Z",
  "url": "https://research.draconitic.com/paper/8634grvhkmhvq",
  "venue": "arXiv",
  "versions": []
}