{"paper":{"title":"A correlation inequality for the expectations of norms of stable vectors","license":"","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Alexander Koldobsky","submitted_at":"1996-03-20T00:00:00Z","abstract_excerpt":"For $0<q\\le 2,\\ 1\\le k < n,$ let $X=(X_1,...,X_n)$ and $Y=(Y_1,...,Y_n)$ be symmetric $q$-stable random vectors so that the joint distributions of $X_1,...,X_k$ and $X_{k+1},...,X_n$ are equal to the joint distributions of $Y_1,...,Y_k$ and $Y_{k+1},...,Y_n,$ respectively, but $Y_i$ and $Y_j$ are independent for every $1\\le i \\le k,\\ k+1\\le j \\le n.$\n  We prove that $\\Bbb E (f(X)) \\ge \\Bbb E (f(Y))$ where $f$ is any continuous, positive, homogeneous of the order $p\\in (-n,0)$ function on $\\Bbb R^n\\setminus \\{0\\}$ such that $f$ is a positive definite distribution in $\\Bbb R^n,$ and $f(u,v)=f(u,"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9603209","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"}