{
  "abstract": "We study the fixed-$q$ right-edge asymptotics of the ordinary $q$-Krawtchouk ensemble. For $0<q<1$, finite polynomial duality gives a direct proof of convergence of the correlation kernels to an explicit limiting kernel. The local Jacobi limit is a shifted continuous $q^{-1}$-Hermite expression with an indeterminate moment problem, so the limiting Jacobi expression does not determine a unique self-adjoint operator. A single spectral atom, asymptotically saturating the mass bound, selects the realization and yields strong-resolvent convergence. The limiting kernel represents its positive spectral projection and admits spectral-series, Christoffel--Darboux, and partial-theta representations. After a ground-state transformation, the associated dual operator agrees with a two-step spatial Markov operator of Borodin--Corwin. For $q>1$, the limiting Jacobi operator is of Al-Salam--Carlitz~I type and is essentially self-adjoint.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.24149",
  "author_total": 1,
  "authors": [
    {
      "name": "Pavel Nikitin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/14r1azdb7exs3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.24149",
  "fulltext_url": null,
  "id": "14r1azdb7exs3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.24149",
  "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-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2604|Mathematical functions and polynomials"
    ]
  ],
  "openalex": "W7213995657",
  "pdf_url": "https://arxiv.org/pdf/2609.24149",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/14r1azdb7exs3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:15Z",
      "native_id": "2609.24149",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.24149"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "The Fixed-$q$ Edge Limit of the $q$-Krawtchouk Ensemble",
  "title_text": "The Fixed-q Edge Limit of the q-Krawtchouk Ensemble",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:19Z",
  "url": "https://research.draconitic.com/paper/14r1azdb7exs3",
  "venue": "arXiv",
  "versions": []
}