{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:ES4QIDVT2NWPEI67LPROHIRSPW","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":"231b3a0d9d861fcec2d824d455e2553319a0e93f009e1d3add5b3bd2c0a265f4","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-24T12:12:17Z","title_canon_sha256":"febbea5b668d1f5bd1f85bb4ec226bd6de63b4cf7f1d7404af080230d0724beb"},"schema_version":"1.0","source":{"id":"1110.5208","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1110.5208","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"arxiv_version","alias_value":"1110.5208v2","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.5208","created_at":"2026-05-18T04:09:55Z"},{"alias_kind":"pith_short_12","alias_value":"ES4QIDVT2NWP","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_16","alias_value":"ES4QIDVT2NWPEI67","created_at":"2026-05-18T12:26:28Z"},{"alias_kind":"pith_short_8","alias_value":"ES4QIDVT","created_at":"2026-05-18T12:26:28Z"}],"graph_snapshots":[{"event_id":"sha256:5196952563fda4e3e19eebbfa7dc9ec76443a6e08a160c786e85eda78e98ea3c","target":"graph","created_at":"2026-05-18T04:09:55Z","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":"Let the sample correlation matrix be $W=YY^T$, where $Y=(y_{ij})_{p,n}$ with $y_{ij}=x_{ij}/\\sqrt{\\sum_{j=1}^nx_{ij}^2}$. We assume $\\{x_{ij}: 1\\leq i\\leq p, 1\\leq j\\leq n\\}$ to be a collection of independent symmetric distributed random variables with sub-exponential tails. Moreover, for any $i$, we assume $x_{ij}, 1\\leq j\\leq n$ to be identically distributed. We assume $0<p<n$ and $p/n\\rightarrow y$ with some $y\\in(0,1)$ as $p,n\\rightarrow\\infty$. In this paper, we provide the Tracy-Widom law ($TW_1$) for both the largest and smallest eigenvalues of $W$. If $x_{ij}$ are i.i.d. standard norma","authors_text":"Guangming Pan, Wang Zhou, Zhigang Bao","cross_cats":["math.PR","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-24T12:12:17Z","title":"Tracy-Widom law for the extreme eigenvalues of sample correlation matrices"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.5208","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:b450fdbac6f40ae336517a64e9c9d1ab800cdf733ea4816142bad2aae1377981","target":"record","created_at":"2026-05-18T04:09:55Z","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":"231b3a0d9d861fcec2d824d455e2553319a0e93f009e1d3add5b3bd2c0a265f4","cross_cats_sorted":["math.PR","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-10-24T12:12:17Z","title_canon_sha256":"febbea5b668d1f5bd1f85bb4ec226bd6de63b4cf7f1d7404af080230d0724beb"},"schema_version":"1.0","source":{"id":"1110.5208","kind":"arxiv","version":2}},"canonical_sha256":"24b9040eb3d36cf223df5be2e3a2327d947f40d8b6cbe2a22462f4948011da29","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"24b9040eb3d36cf223df5be2e3a2327d947f40d8b6cbe2a22462f4948011da29","first_computed_at":"2026-05-18T04:09:55.821732Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T04:09:55.821732Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"of/G2WhHlRKGrzm6+2NhHqjqbGdZvL+xdlpiYbAsE4E6NYBH5MLrDtA4DSFf0ye6gnsirXDVDkJ3BHfpec1iDg==","signature_status":"signed_v1","signed_at":"2026-05-18T04:09:55.822486Z","signed_message":"canonical_sha256_bytes"},"source_id":"1110.5208","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:b450fdbac6f40ae336517a64e9c9d1ab800cdf733ea4816142bad2aae1377981","sha256:5196952563fda4e3e19eebbfa7dc9ec76443a6e08a160c786e85eda78e98ea3c"],"state_sha256":"412bb43f1e92ee510fc5ec2da016ab00feb28f0452fa1026692753bfe46f88cb"}