{"paper":{"title":"Outliers in the spectrum of large deformed unitarily invariant models","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.PR","authors_text":"Hari Bercovici, Maxime F\\'evrier, Mireille Capitaine, Serban Teodor Belinschi","submitted_at":"2012-07-23T16:33:28Z","abstract_excerpt":"We investigate the asymptotic behavior of the eigenvalues of the sum A+U*BU, where A and B are deterministic N by N Hermitian matrices having respective limiting compactly supported distributions \\mu, \\nu, and U is a random N by N unitary matrix distributed according to Haar measure. We assume that A has a fixed number of fixed eigenvalues (spikes) outside the support of \\mu, whereas the distances between the other eigenvalues of A and the support of \\mu, and between the eigenvalues of B and the support of \\nu, uniformly go to zero as N goes to infinity. We establish that only a particular sub"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.5443","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"}