{
  "abstract": "We use the series representation of the Bessel functions of type $B_N$ in terms of Jack polynomials and show that $$\\lim_{k_1\\to\\infty} J_{(k_1,k_2)}^B(x,k_1y)^{1/k_1}= 2^N\\prod\\limits_{i=1}^N \\Bigg( e^{\\sqrt{1+x_i^2 y_i^2}-1}\\cdot \\frac{1}{\\sqrt{1+x_i^2 y_i^2}+1} \\Bigg)$$ for $x,y\\in\\mathbb R^N$ and $k_2\\ge0$. Moreover, the known Laplace-type integral representations for $N\\ge1$ and $k_2=0,1/2,1,2$ and for $N=2$ and $k_2>0$ by Rösler and Demni respectively lead to related limits for $$\\lim_{k_1 \\to \\infty} \\partial_{x_j} J_{(k_1,k_2)}^B(x,k_1y) /(k_1 \\cdot J_{(k_1,k_2)}^B(x,k_1 y)) \\quad (j=1,\\ldots,N).$$ These limits lead to weak limit results for the associated Bessel processes with drift. For $k_2=1/2,1,2$, these limit results have applications to radial parts of Brownian motions with drift on the $M\\times N$-dimensional matrices over $\\mathbb R,\\mathbb C$, and the quaternions for $M\\to\\infty$. We also discuss these limits in the Dunkl case $N=1$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21071",
  "author_total": 2,
  "authors": [
    {
      "name": "Jan Richter"
    },
    {
      "name": "Michael Voit"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7vrprncmztv4k.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21071",
  "fulltext_url": null,
  "id": "7vrprncmztv4k",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21071",
  "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.CA"
    ],
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      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.PR"
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    [
      "arxiv",
      "math.RT"
    ],
    [
      "openalex",
      "2613|Random Matrices and Applications"
    ]
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  "openalex": "W7213946191",
  "pdf_url": "https://arxiv.org/pdf/2609.21071",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7vrprncmztv4k.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:03Z",
      "native_id": "2609.21071",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21071"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.RT",
      "subfield": "algebra-number-theory"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.CA",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Some freezing limits for Bessel functions and Bessel processes with drift of type $B_N$",
  "title_text": "Some freezing limits for Bessel functions and Bessel processes with drift of type B_N",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/7vrprncmztv4k",
  "venue": "arXiv",
  "versions": []
}