{"paper":{"title":"The outliers among the singular values of large rectangular random matrices with additive fixed rank deformation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francois Chapon (IMT), Romain Couillet (SSEC), Walid Hachem (LTCI), Xavier Mestre (CTTC)","submitted_at":"2012-07-02T18:54:36Z","abstract_excerpt":"Consider the matrix $\\Sigma_n = n^{-1/2} X_n D_n^{1/2} + P_n$ where the matrix $X_n \\in \\C^{N\\times n}$ has Gaussian standard independent elements, $D_n$ is a deterministic diagonal nonnegative matrix, and $P_n$ is a deterministic matrix with fixed rank. Under some known conditions, the spectral measures of $\\Sigma_n \\Sigma_n^*$ and $n^{-1} X_n D_n X_n^*$ both converge towards a compactly supported probability measure $\\mu$ as $N,n\\to\\infty$ with $N/n\\to c>0$. In this paper, it is proved that finitely many eigenvalues of $\\Sigma_n\\Sigma_n^*$ may stay away from the support of $\\mu$ in the large"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.0471","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"}