{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:EIJQNEN343ZLDKSR3WTXWDRSOK","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"454ea1a99d308e260481d416ec70127cf7d9e8c99223f25e5faa8513c25a019e","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-08-08T06:33:05Z","title_canon_sha256":"db0cfad3d7b9e632a0495f30571a79047236dc69e431a5aa335c6571b5e17d43"},"schema_version":"1.0","source":{"id":"1308.1766","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1308.1766","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"arxiv_version","alias_value":"1308.1766v2","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1308.1766","created_at":"2026-05-18T03:06:54Z"},{"alias_kind":"pith_short_12","alias_value":"EIJQNEN343ZL","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_16","alias_value":"EIJQNEN343ZLDKSR","created_at":"2026-05-18T12:27:43Z"},{"alias_kind":"pith_short_8","alias_value":"EIJQNEN3","created_at":"2026-05-18T12:27:43Z"}],"graph_snapshots":[{"event_id":"sha256:679efb668880c78aa0b3a2454f8b991ceff290fab8500b560a0d1ab4ab4ef4ce","target":"graph","created_at":"2026-05-18T03:06:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"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. We show that the empir","authors_text":"Debashis Paul, Lili Wang","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-08-08T06:33:05Z","title":"Limiting spectral distribution of renormalized separable sample covariance matrices when $p/n\\to 0$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1766","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:cf12114e61c74c773b31e8306fd7bfb1e82913caef0291e95739cd762c49c705","target":"record","created_at":"2026-05-18T03:06:54Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"454ea1a99d308e260481d416ec70127cf7d9e8c99223f25e5faa8513c25a019e","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2013-08-08T06:33:05Z","title_canon_sha256":"db0cfad3d7b9e632a0495f30571a79047236dc69e431a5aa335c6571b5e17d43"},"schema_version":"1.0","source":{"id":"1308.1766","kind":"arxiv","version":2}},"canonical_sha256":"22130691bbe6f2b1aa51dda77b0e3272a672e83ebe2c5f966cd2f6fc2b3f5e45","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"22130691bbe6f2b1aa51dda77b0e3272a672e83ebe2c5f966cd2f6fc2b3f5e45","first_computed_at":"2026-05-18T03:06:54.640038Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:06:54.640038Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"cORykxlIbpKukelWSdm78au7a4Og9PtsWELr3xKK+h1au/lEPGHEjAoixDdMOIOYmhV5JzQKTtgNrIXPZL4BDw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:06:54.640724Z","signed_message":"canonical_sha256_bytes"},"source_id":"1308.1766","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:cf12114e61c74c773b31e8306fd7bfb1e82913caef0291e95739cd762c49c705","sha256:679efb668880c78aa0b3a2454f8b991ceff290fab8500b560a0d1ab4ab4ef4ce"],"state_sha256":"0e917acf32e39a23b85b1027b05052defafa200ac32af008de06b73b4319a98d"}