{"paper":{"title":"Reduced two-type decomposable critical branching processes with possibly infinite variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Charline Smadi, Vladimir A. Vatutin","submitted_at":"2015-08-26T20:26:18Z","abstract_excerpt":"We consider a Galton-Watson process $\\mathbf{Z}% (n)=(Z_{1}(n),Z_{2}(n))$ with two types of particles. Particles of type 2 may produce offspring of both types while particles of type 1 may produce particles of their own type only. Let $Z_{i}(m,n)$ be the number of particles of type $i$ at time $m<n$ having offspring at time $n$. Assuming that the process is critical and that the variance of the offspring distribution may be infinite we describe the asymptotic behavior, as $m,n\\rightarrow \\infty $ of the law of $\\mathbf{Z}(m,n)=(Z_1(m,n),Z_2(m,n))$ given $\\mathbf{Z}(n)\\neq \\mathbf{0}$. We find "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.06653","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":""},"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"}