{"paper":{"title":"Family size decomposition of genealogical trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Max Grieshammer","submitted_at":"2019-03-07T09:18:00Z","abstract_excerpt":"We study the path of family size decompositions of varying depth of genealogical trees. We prove that this decomposition as a function on (equivalence classes of) ultra-metric measure spaces to the Skorohod space describing the family sizes at different depths is perfect onto its image, i.e. there is a suitable topology such that this map is continuous closed surjective and pre-images of compact sets are compact. We also specify a (dense) subset so that the restriction of the function to this subspace is a homeomorphism. This property allows us to argue that the whole genealogy of a Fleming-Vi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1903.02782","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"}