{"paper":{"title":"Strong asymptotic independence on Wiener chaos","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Nualart, Giovanni Peccati (FSTC), Ivan Nourdin (IECL)","submitted_at":"2014-01-10T08:06:57Z","abstract_excerpt":"Let $F_n = (F_{1,n}, ....,F_{d,n})$, $n\\geq 1$, be a sequence of random vectors such that, for every $j=1,...,d$, the random variable $F_{j,n}$ belongs to a fixed Wiener chaos of a Gaussian field. We show that, as $n\\to\\infty$, the components of $F_n$ are asymptotically independent if and only if ${\\rm Cov}(F_{i,n}^2,F_{j,n}^2)\\to 0$ for every $i\\neq j$. Our findings are based on a novel inequality for vectors of multiple Wiener-It\\^o integrals, and represent a substantial refining of criteria for asymptotic independence in the sense of moments recently established by Nourdin and Rosinski."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2247","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"}