{"paper":{"title":"Fluctuation of matrix entries and application to outliers of elliptic matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Florent Benaych-Georges, Guillaume C\\'ebron, Jean Rochet","submitted_at":"2016-02-09T10:47:24Z","abstract_excerpt":"For any family of $N\\times N$ random matrices $(\\mathbf{A}_k)_{k\\in K}$ which is invariant, in law, under unitary conjugation, we give general sufficient conditions for central limit theorems for random variables of the type $\\operatorname{Tr}(\\mathbf{A}_k \\mathbf{M})$, where the matrix $\\mathbf{M}$ is deterministic (such random variables include for example the normalized matrix entries of the $\\mathbf{A}_k$'s). A consequence is the asymptotic independence of the projection of the matrices $\\mathbf{A}_k$ onto the subspace of null trace matrices from their projections onto the orthogonal of th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.02929","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"}