{"paper":{"title":"Persistence of competing systems of branching random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Zakhar Kabluchko","submitted_at":"2011-03-30T10:07:08Z","abstract_excerpt":"We consider a system of independent branching random walks on $\\R$ which start off a Poisson point process with intensity of the form $e_{\\lambda}(du)=e^{-\\lambda u}du$, where $\\lambda\\in\\R$ is chosen in such a way that the overall intensity of particles is preserved. Denote by $\\chi$ the cluster distribution and let $\\phi$ be the log-Laplace transform of the intensity of $\\chi$. If $\\lambda\\phi'(\\lambda)>0$, we show that the system is persistent (stable) meaning that the point process formed by the particles in the $n$-th generation converges as $n\\to\\infty$ to a non-trivial point process $\\P"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.5865","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"}