{"paper":{"title":"H\\\"older-type inequalities and their applications to concentration and correlation bounds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Christos Pelekis, Jan Ramon, Yuyi Wang","submitted_at":"2015-11-23T12:53:49Z","abstract_excerpt":"Let $Y_v, v\\in V,$ be $[0,1]$-valued random variables having a dependency graph $G=(V,E)$. We show that \\[ \\mathbb{E}\\left[\\prod_{v\\in V} Y_{v} \\right] \\leq \\prod_{v\\in V} \\left\\{ \\mathbb{E}\\left[Y_v^{\\frac{\\chi_b}{b}}\\right] \\right\\}^{\\frac{b}{\\chi_b}}, \\] where $\\chi_b$ is the $b$-fold chromatic number of $G$. This inequality may be seen as a dependency-graph analogue of a generalised H\\\"older inequality, due to Helmut Finner. Additionally, we provide applications of H\\\"older-type inequalities to concentration and correlation bounds for sums of weakly dependent random variables."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1511.07204","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"}