{
  "abstract": "A unified approach for studying the linear eigenvalue statistics (LES) of generalized patterned random matrices was developed in Kumar, Maurya, Saha (2026). In this paper, as a continuation, we develop a unified method for studying the time-dependent LES of generalized patterned random matrices with independent process entries such as Brownian motion and Ornstein-Uhlenbeck process. We prove that if the limiting moment sequence of the LES of the generalized patterned random matrix with independent standard Gaussian entries is M-determinate, then under some minimal assumption on the link function, the time-dependent LES converges to a deterministic real-valued process.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2611.06686",
  "author_total": 3,
  "authors": [
    {
      "name": "Kiran Kumar"
    },
    {
      "name": "Shambhu Nath Maurya"
    },
    {
      "name": "Koushik Saha"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ezbh8yfgdny6w.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2611.06686",
  "fulltext_url": null,
  "id": "ezbh8yfgdny6w",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2611.06686",
  "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"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2611.06686",
  "pmcid": null,
  "pmid": null,
  "published": "2026-11-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ezbh8yfgdny6w.ris",
  "sources": [
    {
      "first_seen": "2026-11-05T15:21:00Z",
      "native_id": "2611.06686",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2611.06686"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "A unified approach to fluctuations of LES of time-dependent generalized patterned random matrices",
  "title_text": "A unified approach to fluctuations of LES of time-dependent generalized patterned random matrices",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:30Z",
  "url": "https://research.draconitic.com/paper/ezbh8yfgdny6w",
  "venue": "arXiv",
  "versions": []
}