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It was shown in arXiv:0710.1346 that if $m,n\\rightarrow \\infty$, $m/n\\rightarrow c\\in \\lbrack 0,\\infty )$, the Normalized Counting Measures of $\\{\\tau _{\\alpha }\\}_{\\alpha =1}^{m}$ converge weakly and $\\{\\mathbf{y}_\\alpha\\}_{\\alpha=1}^m$ are \\textit{good} (see corresponding def"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1310.2506","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-10-09T14:46:59Z","cross_cats_sorted":[],"title_canon_sha256":"d71b02f9db8447abd2d87152d065cfc808db4e2a8525806d791bba34e79505a4","abstract_canon_sha256":"4661c09986bfa21d3fd6f12b0c9b720dc7cae41838e0a653b20b10a6b8679855"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:05:57.454309Z","signature_b64":"HN49dHuNaoVfgJ3KNevrAsjfTsNwNyIWdgK8C3xufdLBZqMvc+z1KHsCIyeOLoygFT53YQbN8/sP/GGyEnpKCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3ed1b23cd6ca7ca23c104d05d453ec9c07e4f45986a614951c95fb383df3b8a7","last_reissued_at":"2026-05-18T03:05:57.453423Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:05:57.453423Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"The Central Limit Theorem for Linear Eigenvalue Statistics of the Sum of Independent Matrices of Rank One","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Lytova, A. Pajor, L. Pastur, O. Gu\\'edon","submitted_at":"2013-10-09T14:46:59Z","abstract_excerpt":"We consider $n\\times n$ random matrices $M_{n}=\\sum_{\\alpha =1}^{m}{\\tau _{\\alpha }}\\mathbf{y}_{\\alpha }\\otimes \\mathbf{y}_{\\alpha }$, where $\\tau _{\\alpha }\\in \\mathbb{R}$, $\\{\\mathbf{y}_{\\alpha }\\}_{\\alpha =1}^{m}$ are i.i.d. isotropic random vectors of $\\mathbb{R}^n$, whose components are not necessarily independent. 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