{
  "abstract": "After centering and scaling, the length of the longest weakly increasing subsequence of a finite-state Markov random word converges to a Brownian last-passage functional with dependent components. We investigate when this functional, and more generally the limiting RSK Young-diagram shape, admits a Gaussian random-matrix representation. We introduce Hermitian Gaussian matrices with correlated diagonal entries and show that isotropy of the Brownian covariance on the trace-zero hyperplane yields such a representation. Within this natural class of Hermitian models with independent Gaussian off-diagonal entries, we prove a rigidity theorem showing that isotropy, together with equality of the off-diagonal variances, characterizes the conditional largest-eigenvalue representation. Explicit three-letter non-cyclic Markov chains demonstrate that this representation is not universal: the limiting Brownian functional may fail to have the law of the largest eigenvalue of any centered jointly Gaussian $3\\times 3$ Hermitian matrix. Finally, we extend the random-matrix identification to chains with non-uniform stationary distributions and to countable state spaces.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.12950",
  "author_total": 2,
  "authors": [
    {
      "name": "Christian Houdré"
    },
    {
      "name": "Dorian Kidonakis"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/csw0k5rs3mh2k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.12950",
  "fulltext_url": null,
  "id": "csw0k5rs3mh2k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.12950",
  "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.CO"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
  ],
  "openalex": "W7221512029",
  "pdf_url": "https://arxiv.org/pdf/2610.12950",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/csw0k5rs3mh2k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:28:40Z",
      "native_id": "2610.12950",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.12950"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Markovian Random Words, a Gaussian Random Matrix Model and Beyond",
  "title_text": "Markovian Random Words, a Gaussian Random Matrix Model and Beyond",
  "type": "preprint",
  "updated_at": "2026-10-30T12:28:40Z",
  "url": "https://research.draconitic.com/paper/csw0k5rs3mh2k",
  "venue": "arXiv",
  "versions": []
}