{"paper":{"title":"Kummer and gamma laws through independences on trees - another parallel with the Matsumoto-Yor property","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Agnieszka Piliszek, Jacek Weso{\\l}owski","submitted_at":"2015-10-31T12:03:49Z","abstract_excerpt":"The paper develops a rather unexpected parallel to the multivariate Matsumoto--Yor (MY) property on trees considered in \\cite{MW04}. The parallel concerns a multivariate version of the Kummer distribution, which is generated by a tree. Given a tree of size $p$, we direct it by choosing a vertex, say $r$, as a root. With such a directed tree we associate a map $\\Phi_r$. For a random vector ${\\bf S}$ having a $p$-variate tree-Kummer distribution and any root $r$, we prove that $\\Phi_r({\\bf S})$ has independent components. Moreover, we show that if ${\\bf S}$ is a random vector in $(0,\\infty)^p$ a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.00116","kind":"arxiv","version":2},"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"}