{"paper":{"title":"Inequalities for sums of random variables in noncommutative probability spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.PR"],"primary_cat":"math.OA","authors_text":"Ghadir Sadeghi, Mohammad Sal Moslehian","submitted_at":"2014-06-12T12:50:29Z","abstract_excerpt":"In this paper, we establish an extension of a noncommutative Bennett inequality with a parameter $1\\leq r\\leq2$ and use it together with some noncommutative techniques to establish a Rosenthal inequality. We also present a noncommutative Hoeffding inequality as follows: Let $(\\mathfrak{M}, \\tau)$ be a noncommutative probability space, $\\mathfrak{N}$ be a von Neumann subalgebra of $\\mathfrak{M}$ with the corresponding conditional expectation $\\mathcal{E}_{\\mathfrak{N}}$ and let subalgebras $\\mathfrak{N}\\subseteq\\mathfrak{A}_j\\subseteq\\mathfrak{M}\\,\\,(j=1, \\cdots, n)$ be successively independent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1406.3220","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"}