{"paper":{"title":"On Random Operator-Valued Matrices: Operator-Valued Semicircular Mixtures and Central Limit Theorem","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Mario Diaz","submitted_at":"2014-10-13T20:16:00Z","abstract_excerpt":"Motivated by a random matrix theory model from wireless communications, we define random operator-valued matrices as the elements of $L^{\\infty-}(\\Omega,{\\mathcal F},{\\mathbb P}) \\otimes M_d({\\mathcal A})$ where $(\\Omega,{\\mathcal F},{\\mathbb P})$ is a classical probability space and $({\\mathcal A},\\varphi)$ is a non-commutative probability space. A central limit theorem for the mean $M_d(\\mathbb{C})$-valued moments of these random operator-valued matrices is derived. Also a numerical algorithm to compute the mean $M_d({\\mathbb C})$-valued Cauchy transform of operator-valued semicircular mixtu"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.3500","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"}