{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:VRSRXM4KPMKGKMMRIU2PLE4APS","short_pith_number":"pith:VRSRXM4K","schema_version":"1.0","canonical_sha256":"ac651bb38a7b146531914534f593807cb24b72d40ea92484b4851487984006b0","source":{"kind":"arxiv","id":"1110.1284","version":3},"attestation_state":"computed","paper":{"title":"On the Rate of Convergence to the Marchenko--Pastur Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2011-10-06T14:52:33Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})$ denote $n\\times p$ random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le n,1\\le k\\le p$. We consider the rate of convergence of empirical spectral distribution function of the matrix $\\mathbf W=\\frac1p\\mathbf X\\mathbf X^*$ to the Marchenko--Pastur law. We assume that $\\mathbf E X_{jk}=0$, $\\mathbf E X_{jk}^2=1$ and that the distributions of the matrix elements $X_{jk}$ have a uniformly sub exponential decay in the sense that there exists a constant $\\varkappa>0$ such that for any $1\\le j \\le n,\\,1\\le k\\le p $ and any $t\\ge 1$ we have $$ \\mathbf{ Pr}"},"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":"1110.1284","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-10-06T14:52:33Z","cross_cats_sorted":[],"title_canon_sha256":"4b9b69d621c541645f0c66d53d70beab4a3112ed662a4ff62f97e670b24ac536","abstract_canon_sha256":"af1b1ff38e57e1b422c4c312eca794715c7e9b37f0a40dd8b0533820fddba615"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:55.294047Z","signature_b64":"Eq+bjvQVEmeApQFpNrGJBcxNB+GCI00dPKvFVxK0XCeJVBOWHXfegVb22aeWn+eWWDBhYFJFffu7xohjJzspBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ac651bb38a7b146531914534f593807cb24b72d40ea92484b4851487984006b0","last_reissued_at":"2026-05-18T02:30:55.293332Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:55.293332Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the Rate of Convergence to the Marchenko--Pastur Distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2011-10-06T14:52:33Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})$ denote $n\\times p$ random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le n,1\\le k\\le p$. We consider the rate of convergence of empirical spectral distribution function of the matrix $\\mathbf W=\\frac1p\\mathbf X\\mathbf X^*$ to the Marchenko--Pastur law. We assume that $\\mathbf E X_{jk}=0$, $\\mathbf E X_{jk}^2=1$ and that the distributions of the matrix elements $X_{jk}$ have a uniformly sub exponential decay in the sense that there exists a constant $\\varkappa>0$ such that for any $1\\le j \\le n,\\,1\\le k\\le p $ and any $t\\ge 1$ we have $$ \\mathbf{ Pr}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.1284","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"1110.1284","created_at":"2026-05-18T02:30:55.293454+00:00"},{"alias_kind":"arxiv_version","alias_value":"1110.1284v3","created_at":"2026-05-18T02:30:55.293454+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1110.1284","created_at":"2026-05-18T02:30:55.293454+00:00"},{"alias_kind":"pith_short_12","alias_value":"VRSRXM4KPMKG","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_16","alias_value":"VRSRXM4KPMKGKMMR","created_at":"2026-05-18T12:26:44.992195+00:00"},{"alias_kind":"pith_short_8","alias_value":"VRSRXM4K","created_at":"2026-05-18T12:26:44.992195+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1907.08880","citing_title":"Spectral Graph Matching and Regularized Quadratic Relaxations I: The Gaussian Model","ref_index":10,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS","json":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS.json","graph_json":"https://pith.science/api/pith-number/VRSRXM4KPMKGKMMRIU2PLE4APS/graph.json","events_json":"https://pith.science/api/pith-number/VRSRXM4KPMKGKMMRIU2PLE4APS/events.json","paper":"https://pith.science/paper/VRSRXM4K"},"agent_actions":{"view_html":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS","download_json":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS.json","view_paper":"https://pith.science/paper/VRSRXM4K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1110.1284&json=true","fetch_graph":"https://pith.science/api/pith-number/VRSRXM4KPMKGKMMRIU2PLE4APS/graph.json","fetch_events":"https://pith.science/api/pith-number/VRSRXM4KPMKGKMMRIU2PLE4APS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS/action/storage_attestation","attest_author":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS/action/author_attestation","sign_citation":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS/action/citation_signature","submit_replication":"https://pith.science/pith/VRSRXM4KPMKGKMMRIU2PLE4APS/action/replication_record"}},"created_at":"2026-05-18T02:30:55.293454+00:00","updated_at":"2026-05-18T02:30:55.293454+00:00"}