{"paper":{"title":"Convergence of a Critical Multitype Bellman--Harris Process with One Infinite-Mean Lifetime","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Prates Machado Fabio, Ram\\'irez-Gonz\\'alez J.H.","submitted_at":"2026-06-09T23:14:59Z","abstract_excerpt":"We study a critical multitype Bellman--Harris branching particle system in $\\mathbb R^N$ with a finite type space $\\mathbb K=\\{1,\\dots,K\\}$. Particles of type $i$ move according to a symmetric $\\alpha_i$-stable process and reproduce according to a critical offspring law whose mean matrix is irreducible and stochastic. The lifetime distribution of type $1$ is assumed to have infinite mean with regularly varying tail $$\n  1-F_1(t)\\sim c_1t^{-\\gamma},\\, 0<\\gamma<1, $$ whereas the remaining lifetime distributions satisfy polynomial upper-tail bounds\n  $$\n  \\overline F_i(t)\\le C t^{-\\eta_i},\\, i=2,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.11511","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.11511/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}