{"paper":{"title":"Stochastic Ordering of Infinite Geometric Galton-Watson Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Erik I. Broman","submitted_at":"2015-02-26T18:09:28Z","abstract_excerpt":"We consider Galton-Watson trees with Geom$(p)$ offspring distribution. We let $T_{\\infty}(p)$ denote such a tree conditioned on being infinite. We prove that for any $1/2\\leq p_1 <p_2 \\leq 1$, there exists a coupling between $T_{\\infty}(p_1)$ and $T_{\\infty}(p_2)$ such that ${\\mathbb P}(T_{\\infty}(p_1) \\subseteq T_{\\infty}(p_2))=1.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.07657","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"}