{"paper":{"title":"Cumulants in Noncommutative Probability Theory IV. De Finetti's Theorem and $L^p$-Inequalities","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.OA","authors_text":"Franz Lehner","submitted_at":"2004-09-02T10:06:13Z","abstract_excerpt":"In this paper we collect a few results about exchangeability systems in which crossing cumulants vanish, which we call noncrossing exchangeability systems. The main result is a free version of De Finetti's theorem, characterising amalgamated free products as noncrossing exchangeability systems which satisfy a so-called weak singleton condition. The main tool in the proof is an $L^p$-inequality with uniformly bounded constants for i.i.d. sequences in noncrossing exchangeability systems."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0409025","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"}