{"paper":{"title":"A representation of exchangeable hierarchies by sampling from real trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chris Haulk, Jim Pitman, Noah Forman","submitted_at":"2011-01-28T20:45:07Z","abstract_excerpt":"A hierarchy on a set $S$, also called a total partition of $S$, is a collection $\\mathcal{H}$ of subsets of $S$ such that $S \\in \\mathcal{H}$, each singleton subset of $S$ belongs to $\\mathcal{H}$, and if $A, B \\in \\mathcal{H}$ then $A \\cap B$ equals either $A$ or $B$ or $\\varnothing$. Every exchangeable random hierarchy of positive integers has the same distribution as a random hierarchy $\\mathcal{H}$ associated as follows with a random real tree $\\mathcal{T}$ equipped with root element $0$ and a random probability distribution $p$ on the Borel subsets of $\\mathcal{T}$: given $(\\mathcal{T},p)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.5619","kind":"arxiv","version":4},"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"}