{"paper":{"title":"Large Deviations for Random Matricial Moment Problems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alain Rouault, Fabrice Gamboa, Jan Nagel, Jens Wagener","submitted_at":"2010-11-01T12:03:13Z","abstract_excerpt":"We consider the moment space $\\mathcal{M}_n^{K}$ corresponding to $p \\times p$ complex matrix measures defined on $K$ ($K=[0,1]$ or $K=\\D$). We endow this set with the uniform law. We are mainly interested in large deviations principles (LDP) when $n \\rightarrow \\infty$. First we fix an integer $k$ and study the vector of the first $k$ components of a random element of $\\mathcal{M}_n^{K}$. We obtain a LDP in the set of $k$-arrays of $p\\times p$ matrices. Then we lift a random element of $\\mathcal{M}_n^{K}$ into a random measure and prove a LDP at the level of random measures. We end with a LDP"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1011.0299","kind":"arxiv","version":3},"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"}