{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:Z2D7E3J4I2EA5GN67G47P7N5PT","short_pith_number":"pith:Z2D7E3J4","schema_version":"1.0","canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","source":{"kind":"arxiv","id":"1405.7820","version":4},"attestation_state":"computed","paper":{"title":"Optimal Bounds for Convergence of Expected Spectral Distributions to the Semi-Circular Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2014-05-30T10:49:27Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le k\\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\\mathbf X$ to the semi-circular law assuming that ${\\mathbf E} X_{jk}=0$, ${\\mathbf E} X_{jk}^2=1$ and that $$ \\sup_{n\\ge1}\\sup_{1\\le j,k\\le n}{\\mathbf E}|X_{jk}|^4=:\\mu_4<\\infty \\quad \\text{and} \\sup_{1\\le j,k\\le n}|X_{jk}|\\le D_0n^{\\frac14}. $$ By means of a recursion argument it is shown that the Kolmogorov distance between the expected spectral distribution "},"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":"1405.7820","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-30T10:49:27Z","cross_cats_sorted":["math.SP"],"title_canon_sha256":"7cfc183cee13cc1a139487583df05e4aa404b3c0641f21bfbe46298a753c4516","abstract_canon_sha256":"1ce798f60038c1b5d48ade666ab36076e47e9452cdc082e4971723f0cc155133"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:37:28.768022Z","signature_b64":"Wu8GSWJdfhP4dsQC+bhVPRP3bz1tL/IhrJjxUWUFF4bCROI0xHOjsGk4uREJg0KkO025pUwNQclaVPSWWxOLAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ce87f26d3c46880e99bef9b9f7fdbd7cf7d9741363ddf1b5212760fdbde3972c","last_reissued_at":"2026-05-18T01:37:28.767453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:37:28.767453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Optimal Bounds for Convergence of Expected Spectral Distributions to the Semi-Circular Law","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.SP"],"primary_cat":"math.PR","authors_text":"A. Tikhomirov, F. G\\\"otze","submitted_at":"2014-05-30T10:49:27Z","abstract_excerpt":"Let $\\mathbf X=(X_{jk})_{j,k=1}^n$ denote a Hermitian random matrix with entries $X_{jk}$, which are independent for $1\\le j\\le k\\le n$. We consider the rate of convergence of the empirical spectral distribution function of the matrix $\\mathbf X$ to the semi-circular law assuming that ${\\mathbf E} X_{jk}=0$, ${\\mathbf E} X_{jk}^2=1$ and that $$ \\sup_{n\\ge1}\\sup_{1\\le j,k\\le n}{\\mathbf E}|X_{jk}|^4=:\\mu_4<\\infty \\quad \\text{and} \\sup_{1\\le j,k\\le n}|X_{jk}|\\le D_0n^{\\frac14}. $$ By means of a recursion argument it is shown that the Kolmogorov distance between the expected spectral distribution "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.7820","kind":"arxiv","version":4},"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":"1405.7820","created_at":"2026-05-18T01:37:28.767534+00:00"},{"alias_kind":"arxiv_version","alias_value":"1405.7820v4","created_at":"2026-05-18T01:37:28.767534+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1405.7820","created_at":"2026-05-18T01:37:28.767534+00:00"},{"alias_kind":"pith_short_12","alias_value":"Z2D7E3J4I2EA","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"Z2D7E3J4I2EA5GN6","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"Z2D7E3J4","created_at":"2026-05-18T12:28:59.999130+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/Z2D7E3J4I2EA5GN67G47P7N5PT","json":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT.json","graph_json":"https://pith.science/api/pith-number/Z2D7E3J4I2EA5GN67G47P7N5PT/graph.json","events_json":"https://pith.science/api/pith-number/Z2D7E3J4I2EA5GN67G47P7N5PT/events.json","paper":"https://pith.science/paper/Z2D7E3J4"},"agent_actions":{"view_html":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT","download_json":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT.json","view_paper":"https://pith.science/paper/Z2D7E3J4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1405.7820&json=true","fetch_graph":"https://pith.science/api/pith-number/Z2D7E3J4I2EA5GN67G47P7N5PT/graph.json","fetch_events":"https://pith.science/api/pith-number/Z2D7E3J4I2EA5GN67G47P7N5PT/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/action/timestamp_anchor","attest_storage":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/action/storage_attestation","attest_author":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/action/author_attestation","sign_citation":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/action/citation_signature","submit_replication":"https://pith.science/pith/Z2D7E3J4I2EA5GN67G47P7N5PT/action/replication_record"}},"created_at":"2026-05-18T01:37:28.767534+00:00","updated_at":"2026-05-18T01:37:28.767534+00:00"}