{
  "abstract": "We study a critical multitype branching particle system in $\\mathbb{R}^N$ with finite type space $\\mathcal{K}={1,\\dots,K}$. Particles of type $i$ move according to a symmetric $α_i$-stable process and reproduce according to a critical offspring law with irreducible stochastic mean matrix. All lifetime distributions are non-arithmetic. The type-$1$ lifetime distribution has infinite mean and a regularly varying tail $$ 1-F_1(t)\\sim c_1t^{-γ}, \\qquad 0<γ<1, $$ whereas the lifetime distributions of types $2,\\dots,K$ satisfy the polynomial upper-tail bounds $$ 1-F_i(t)\\le C t^{-η_i}, \\qquad i=2,\\dots,K, \\qquad η_i>1, \\qquad η:=\\min_{2\\le i\\le K}η_i. $$ The offspring mechanism satisfies a $(1+β)$-stable-domain regular-variation condition, with $β\\in(0,1]$. The initial population is a Poisson random measure with intensity $$ Λ=\\sum_{i=1}^K a_i\\,λ\\otimesδ_i, \\qquad a_i\\ge0, $$ and we set $A:=\\sum_{i=1}^K a_i$. Under the space--lifetime condition $$ ρ:=\\left(η-1\\right)\\wedge\\frac{N}{α_1} > \\fracγβ, $$ we prove that the system converges to a Poisson random measure with intensity $Aλ\\otimesδ_1$. Thus, although the initial population may assign positive spatial intensity to every type, the limiting population is supported entirely on the infinite-mean type while preserving the aggregate initial spatial intensity $Aλ$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2606.11511",
  "author_total": 2,
  "authors": [
    {
      "name": "Ramírez-González J. H."
    },
    {
      "name": "Prates Machado Fabio"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/1wvtbyf364seb.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2606.11511",
  "fulltext_url": null,
  "id": "1wvtbyf364seb",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2606.11511",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.PR"
    ],
    [
      "openalex",
      "2610|Stochastic processes and statistical mechanics"
    ]
  ],
  "openalex": "W7164358713",
  "pdf_url": "https://arxiv.org/pdf/2606.11511",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-03",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/1wvtbyf364seb.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2606.11511",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2606.11511"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Convergence of a Critical Multitype Branching Particle System with Mixed Finite and Infinite Mean Lifetimes",
  "title_text": "Convergence of a Critical Multitype Branching Particle System with Mixed Finite and Infinite Mean Lifetimes",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/1wvtbyf364seb",
  "venue": "arXiv",
  "versions": []
}