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We consider simultaneously $R$ sample covariance matrices $\\mathbf{B}_{nr}=\\frac1n \\mathbf{Q}_r \\mathbf{X}_n \\mathbf{X}_n^*\\mathbf{Q}_r^\\top,~1\\le r\\le R$, where the $\\mathbf{Q}_{r}$'s are nonrandom real matrices with common dimensions $p\\times k~(k\\geq p)$. Assuming that both the dimension $p$ and the sample size $n$ grow to infinity, the limiting distributions of the eigenvalues of the matrices $\\{\\mathbf{B}_{nr}\\}$ are identified, "},"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":"1801.06634","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2018-01-20T06:27:59Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"b8a26abfb79d9042fdf16c40a42c3bfdb99cb86ba3a09cf62edca167cd75d5a1","abstract_canon_sha256":"7d62d87eaa1e46bc0f0f0d1cf5b9521b5662db30c1ccbea95f165e00e1e96b5c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:25:28.149166Z","signature_b64":"6xlSy+QoDb9/RXbqMYQn1xAxhqPtmtqjunK1sG3ldxiajRUuj+DmQC7IRXjZZotkWV2FxbJZuodzx1wc6vvlCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"8e337380bae3796efc05720cb0c4ad9a761bc28de6e77b17036829ecefb4763c","last_reissued_at":"2026-05-18T00:25:28.148518Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:25:28.148518Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Joint CLT for eigenvalue statistics from several dependent large dimensional sample covariance matrices with application","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Jianfeng Yao, Weiming Li, Zeng Li","submitted_at":"2018-01-20T06:27:59Z","abstract_excerpt":"Let $\\mathbf{X}_n=(x_{ij})$ be a $k \\times n$ data matrix with complex-valued, independent and standardized entries satisfying a Lindeberg-type moment condition. 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