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We prove that the moments of fluctuations normalized by $n^{-1/2}$ in the limit $n\\to\\infty$ satisfy the Wick relations for the Gaussian random variables. This allows us to prove central limit theorem for $\\hbox{Tr}G(z)$ and then extend the result on the linear eigenvalue statistics $\\hbox{Tr}\\phi(A)$ of any function $\\phi:\\mathbb{R}\\to\\mathbb{R}$ which increases, together with its first two derivatives, at infinity n"},"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":"0911.5684","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2009-11-30T16:25:00Z","cross_cats_sorted":["math.MP"],"title_canon_sha256":"deb3af69f5cdf6b56c8054dd47db0922c0e653bc035cbe43d173228b723d10f3","abstract_canon_sha256":"9bcad2602c82eb9b25e4e705603e25d8e322d904736bcc959e83e3654b4c5208"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:10:35.507607Z","signature_b64":"Fwrx3KEv7tLqiCqaCnxm0VbN2bNMo6VgdNveARGzPHVKnjbSunKLGdPV593csHYRp54xEkQSSJhwbIoJDKqZCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"ad95272063772360f1d17c95781d83f1a53a9a30dea8be0e8062d0c0058c887b","last_reissued_at":"2026-05-18T02:10:35.506839Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:10:35.506839Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Central limit theorem for fluctuations of linear eigenvalue statistics of large random graphs","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"B. 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This allows us to prove central limit theorem for $\\hbox{Tr}G(z)$ and then extend the result on the linear eigenvalue statistics $\\hbox{Tr}\\phi(A)$ of any function $\\phi:\\mathbb{R}\\to\\mathbb{R}$ which increases, together with its first two derivatives, at infinity n"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0911.5684","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":"0911.5684","created_at":"2026-05-18T02:10:35.506949+00:00"},{"alias_kind":"arxiv_version","alias_value":"0911.5684v1","created_at":"2026-05-18T02:10:35.506949+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0911.5684","created_at":"2026-05-18T02:10:35.506949+00:00"},{"alias_kind":"pith_short_12","alias_value":"VWKSOIDDO4RW","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_16","alias_value":"VWKSOIDDO4RWB4OR","created_at":"2026-05-18T12:26:02.257875+00:00"},{"alias_kind":"pith_short_8","alias_value":"VWKSOIDD","created_at":"2026-05-18T12:26:02.257875+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/VWKSOIDDO4RWB4ORPSKXQHMD6G","json":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G.json","graph_json":"https://pith.science/api/pith-number/VWKSOIDDO4RWB4ORPSKXQHMD6G/graph.json","events_json":"https://pith.science/api/pith-number/VWKSOIDDO4RWB4ORPSKXQHMD6G/events.json","paper":"https://pith.science/paper/VWKSOIDD"},"agent_actions":{"view_html":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G","download_json":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G.json","view_paper":"https://pith.science/paper/VWKSOIDD","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0911.5684&json=true","fetch_graph":"https://pith.science/api/pith-number/VWKSOIDDO4RWB4ORPSKXQHMD6G/graph.json","fetch_events":"https://pith.science/api/pith-number/VWKSOIDDO4RWB4ORPSKXQHMD6G/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G/action/timestamp_anchor","attest_storage":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G/action/storage_attestation","attest_author":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G/action/author_attestation","sign_citation":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G/action/citation_signature","submit_replication":"https://pith.science/pith/VWKSOIDDO4RWB4ORPSKXQHMD6G/action/replication_record"}},"created_at":"2026-05-18T02:10:35.506949+00:00","updated_at":"2026-05-18T02:10:35.506949+00:00"}