{"paper":{"title":"Algebraic methods toward higher-order probability inequalities, II","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Donald St. P. Richards","submitted_at":"2004-10-06T12:19:26Z","abstract_excerpt":"Let (L,\\preccurlyeq) be a finite distributive lattice, and suppose that the functions f_1,f_2:L\\to R are monotone increasing with respect to the partial order \\preccurlyeq. Given \\mu a probability measure on L, denote by E(f_i) the average of f_i over L with respect to \\mu, i=1,2. Then the\n FKG inequality provides a condition on the measure \\mu under which the covariance, Cov(f_1,f_2):=E(f_1f_2)-E(f_1)E(f_2), is nonnegative. In this paper we derive a ``third-order'' generalization of the FKG inequality.\n We also establish fourth- and fifth-order generalizations of the FKG inequality and formul"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0410155","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"}