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We show that the empir"},"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":"1308.1766","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-08-08T06:33:05Z","cross_cats_sorted":["math.PR","stat.TH"],"title_canon_sha256":"db0cfad3d7b9e632a0495f30571a79047236dc69e431a5aa335c6571b5e17d43","abstract_canon_sha256":"454ea1a99d308e260481d416ec70127cf7d9e8c99223f25e5faa8513c25a019e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:06:54.640724Z","signature_b64":"cORykxlIbpKukelWSdm78au7a4Og9PtsWELr3xKK+h1au/lEPGHEjAoixDdMOIOYmhV5JzQKTtgNrIXPZL4BDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"22130691bbe6f2b1aa51dda77b0e3272a672e83ebe2c5f966cd2f6fc2b3f5e45","last_reissued_at":"2026-05-18T03:06:54.640038Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:06:54.640038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Limiting spectral distribution of renormalized separable sample covariance matrices when $p/n\\to 0$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","stat.TH"],"primary_cat":"math.ST","authors_text":"Debashis Paul, Lili Wang","submitted_at":"2013-08-08T06:33:05Z","abstract_excerpt":"We are concerned with the behavior of the eigenvalues of renormalized sample covariance matrices of the form C_n=\\sqrt{\\frac{n}{p}}\\left(\\frac{1}{n}A_{p}^{1/2}X_{n}B_{n}X_{n}^{*}A_{p}^{1/2}-\\frac{1}{n}\\tr(B_{n})A_{p}\\right) as $p,n\\to \\infty$ and $p/n\\to 0$, where $X_{n}$ is a $p\\times n$ matrix with i.i.d. real or complex valued entries $X_{ij}$ satisfying $E(X_{ij})=0$, $E|X_{ij}|^2=1$ and having finite fourth moment. $A_{p}^{1/2}$ is a square-root of the nonnegative definite Hermitian matrix $A_{p}$, and $B_{n}$ is an $n\\times n$ nonnegative definite Hermitian matrix. 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