{"paper":{"title":"Inequalities of correlation type for symmetric stable random vectors","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alexander Koldobsky, Stephen J. Montgomery-Smith","submitted_at":"1995-03-02T20:10:40Z","abstract_excerpt":"We prove that, for any jointly stable random variables $X_1, \\dots, X_k$ with zero mean, any $m<k,$ and any even continuous positive definite functions $f$ and $g$ on $\\Bbb R^m$ and $\\Bbb R^{k-m},$ the random variables $f(X_1,\\dots,X_m)$ and $g(X_{m+1}, \\dots,X_k)$ are non-negatively correlated. We also show another result that is related to an old question of whether $$P(\\max_{1\\le i\\le k} |X_i|<t) \\ge P(\\max_{1\\le i\\le m} |X_i|<t) \\ P(\\max_{m+1\\le i\\le k} |X_i|<t)$$ where $X_1,\\dots,X_k$ are jointly Gaussian random variables with zero mean, and $m<k.$ We show that the quantity in the left-ha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9503212","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"}