{"paper":{"title":"Proof of Gaussian moment product conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xiangfeng Yang","submitted_at":"2016-09-29T13:31:18Z","abstract_excerpt":"For an $n$-dimensional real-valued centered Gaussian random vector $(X_1,\\ldots,X_n)$ with any covariance matrix, the following moment product conjecture is proved in this paper \\[ \\mathbb{E}\\prod_{j=1}^nX_j^{2m_j}\\geq \\prod_{j=1}^n\\mathbb{E}X_j^{2m_j}, \\] where $m_j\\geq1,1\\leq j\\leq n,$ are any positive integers. Among other important applications, a special case of this conjecture (with $m_j=m,1\\leq j\\leq n$) would give an affirmative answer to another open problem: real linear polarization constant. The proof is based on a very elegant and elementary approach in which only one component $X_"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.09328","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"}