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For those values of $n,p$ we investigate the rate of convergence of the expected spectral distribution function of the matrix $\\mathbf W=\\frac1{ p}\\mathbf X\\mathbf X^*$ to the Marchenko-Pastur law with parameter $y$. Assuming the conditions $\\mathbf E X_{jk}=0$, $\\mathbf E X_{jk}^2=1$ and $ \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\sup_{n,p\\ge1}\\sup_{1\\le j\\le n,1\\le k\\le p}\\mathbf E |X_{jk"},"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":"1412.6284","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-12-19T10:49:21Z","cross_cats_sorted":[],"title_canon_sha256":"1225376b0ff22338cf6e1702eab99a537e7b3626d09c33f94f2c08931fb3591e","abstract_canon_sha256":"30aa7fd1dbb8cfa4f48ec4e6a49a9039ef88b9b5324ed89645256422aa4bff37"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:30:53.889551Z","signature_b64":"WAwhP+8T4M8kYopc+6aCGtBHl4VDrVkJivxG/q11JlmdRjtiwBVp0lBQojRSDkH6SjIZBcdwGtlmzv+YtAmDAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e351ef0dc81719eb0f47dcf594c77dea08c8f6a1932da85960ecd6f349325ef9","last_reissued_at":"2026-05-18T02:30:53.888929Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:30:53.888929Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Rate of Convergence of the Expected Spectral Distribution Function to the Marchenko -- Pastur Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"A.N. Tikhomirov, F. G\\\"otze","submitted_at":"2014-12-19T10:49:21Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})$ denote a $n\\times p$ random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le n, 1\\le k\\le p$. Let $n,p$ tend to infinity such that $\\frac np=y+O(n^{-1})\\in(0,1]$. For those values of $n,p$ we investigate the rate of convergence of the expected spectral distribution function of the matrix $\\mathbf W=\\frac1{ p}\\mathbf X\\mathbf X^*$ to the Marchenko-Pastur law with parameter $y$. Assuming the conditions $\\mathbf E X_{jk}=0$, $\\mathbf E X_{jk}^2=1$ and $ \\quad \\quad \\quad \\quad \\quad \\quad \\quad \\sup_{n,p\\ge1}\\sup_{1\\le j\\le n,1\\le k\\le p}\\mathbf E |X_{jk"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.6284","kind":"arxiv","version":1},"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":"1412.6284","created_at":"2026-05-18T02:30:53.889028+00:00"},{"alias_kind":"arxiv_version","alias_value":"1412.6284v1","created_at":"2026-05-18T02:30:53.889028+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1412.6284","created_at":"2026-05-18T02:30:53.889028+00:00"},{"alias_kind":"pith_short_12","alias_value":"4NI66DOIC4M6","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_16","alias_value":"4NI66DOIC4M6WD2H","created_at":"2026-05-18T12:28:14.216126+00:00"},{"alias_kind":"pith_short_8","alias_value":"4NI66DOI","created_at":"2026-05-18T12:28:14.216126+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I","json":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I.json","graph_json":"https://pith.science/api/pith-number/4NI66DOIC4M6WD2H3T2ZJR355I/graph.json","events_json":"https://pith.science/api/pith-number/4NI66DOIC4M6WD2H3T2ZJR355I/events.json","paper":"https://pith.science/paper/4NI66DOI"},"agent_actions":{"view_html":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I","download_json":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I.json","view_paper":"https://pith.science/paper/4NI66DOI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1412.6284&json=true","fetch_graph":"https://pith.science/api/pith-number/4NI66DOIC4M6WD2H3T2ZJR355I/graph.json","fetch_events":"https://pith.science/api/pith-number/4NI66DOIC4M6WD2H3T2ZJR355I/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I/action/storage_attestation","attest_author":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I/action/author_attestation","sign_citation":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I/action/citation_signature","submit_replication":"https://pith.science/pith/4NI66DOIC4M6WD2H3T2ZJR355I/action/replication_record"}},"created_at":"2026-05-18T02:30:53.889028+00:00","updated_at":"2026-05-18T02:30:53.889028+00:00"}