{
  "abstract": "We consider the general mother-dependent neutral mutation model defined in Blancas, Fittipaldi and Hernández-Torres (2026), consisting of a multitype branching process in which every individual carries one of $d$ alleles and each mutant child acquires a type different from that of its mother, according to a prescribed distribution. We assume that the total offspring distribution is critical and belongs to the domain of attraction of an $α$-stable law, with $α\\in(1,2)$, while mutations are rare. Extending the results of Blancas and Rivero (2018), we prove the finite-dimensional convergence of the rescaled Markov chain that records, in each allelic generation, the sizes of the type-specific clone subfamilies and the mutant populations they produce. The limiting clone masses form a multitype Jiřina process driven by stable subordinators with drift, whose branching mechanism combines the stable reproduction law with the mother-dependent mutation matrix.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.37815",
  "author_total": 2,
  "authors": [
    {
      "name": "Airam Blancas"
    },
    {
      "name": "María Clara Fittipaldi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/3zhdbkhvay68j.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.37815",
  "fulltext_url": null,
  "id": "3zhdbkhvay68j",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.37815",
  "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/2610.37815",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-27",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/3zhdbkhvay68j.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2610.37815",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.37815"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stable limits for the clone-mutant chain with mother-dependent mutation",
  "title_text": "Stable limits for the clone-mutant chain with mother-dependent mutation",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/3zhdbkhvay68j",
  "venue": "arXiv",
  "versions": []
}