{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2010:ICJXTUFS2ZEWFIU7OE33LCPHWS","short_pith_number":"pith:ICJXTUFS","schema_version":"1.0","canonical_sha256":"409379d0b2d64962a29f7137b589e7b4b73da5cb98e7d4129726549364e5b8f2","source":{"kind":"arxiv","id":"1003.5996","version":1},"attestation_state":"computed","paper":{"title":"Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Christophe Carr\\'e, Jean-Gabriel Luque, Matthieu Deneufchatel, Pierpaolo Vivo","submitted_at":"2010-03-31T09:20:55Z","abstract_excerpt":"We investigate the asymptotic behavior of the Selberg-like integral $$ \\frac1{N!}\\int_{[0,1]^N}x_1^p\\prod_{i<j}(x_i-x_j)^2\\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i$$, as $N\\to\\infty$ for different scalings of the parameters $a$ and $b$ with $N$. Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting $N$ channels in the two attached leads. Making use of Newton's interpolation formula, we show that an asymptotic limit exists and we compute it explicitly."},"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":"1003.5996","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math-ph","submitted_at":"2010-03-31T09:20:55Z","cross_cats_sorted":["cond-mat.mes-hall","math.CO","math.MP"],"title_canon_sha256":"3a94cf185e8a148902240f7cf13bc4abf011673628afb765ff48878ed67c550e","abstract_canon_sha256":"6aee47b577031653bee3872ccdbb6a04018c08a50f53093436966c3c2266d4ec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:08:15.530172Z","signature_b64":"2d/qTmfGgPIVfZL296v+JMoYhcn8aPe8LlFT4Om77dJnCAwwJNtBQVJUu+0WH13RgE1cz3XQlpgKRM2KVfYHCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"409379d0b2d64962a29f7137b589e7b4b73da5cb98e7d4129726549364e5b8f2","last_reissued_at":"2026-05-18T02:08:15.529766Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:08:15.529766Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotics of Selberg-like integrals: The unitary case and Newton's interpolation formula","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cond-mat.mes-hall","math.CO","math.MP"],"primary_cat":"math-ph","authors_text":"Christophe Carr\\'e, Jean-Gabriel Luque, Matthieu Deneufchatel, Pierpaolo Vivo","submitted_at":"2010-03-31T09:20:55Z","abstract_excerpt":"We investigate the asymptotic behavior of the Selberg-like integral $$ \\frac1{N!}\\int_{[0,1]^N}x_1^p\\prod_{i<j}(x_i-x_j)^2\\prod_ix_i^{a-1}(1-x_i)^{b-1}dx_i$$, as $N\\to\\infty$ for different scalings of the parameters $a$ and $b$ with $N$. Integrals of this type arise in the random matrix theory of electronic scattering in chaotic cavities supporting $N$ channels in the two attached leads. Making use of Newton's interpolation formula, we show that an asymptotic limit exists and we compute it explicitly."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1003.5996","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":"1003.5996","created_at":"2026-05-18T02:08:15.529835+00:00"},{"alias_kind":"arxiv_version","alias_value":"1003.5996v1","created_at":"2026-05-18T02:08:15.529835+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1003.5996","created_at":"2026-05-18T02:08:15.529835+00:00"},{"alias_kind":"pith_short_12","alias_value":"ICJXTUFS2ZEW","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_16","alias_value":"ICJXTUFS2ZEWFIU7","created_at":"2026-05-18T12:26:09.077623+00:00"},{"alias_kind":"pith_short_8","alias_value":"ICJXTUFS","created_at":"2026-05-18T12:26:09.077623+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/ICJXTUFS2ZEWFIU7OE33LCPHWS","json":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS.json","graph_json":"https://pith.science/api/pith-number/ICJXTUFS2ZEWFIU7OE33LCPHWS/graph.json","events_json":"https://pith.science/api/pith-number/ICJXTUFS2ZEWFIU7OE33LCPHWS/events.json","paper":"https://pith.science/paper/ICJXTUFS"},"agent_actions":{"view_html":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS","download_json":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS.json","view_paper":"https://pith.science/paper/ICJXTUFS","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1003.5996&json=true","fetch_graph":"https://pith.science/api/pith-number/ICJXTUFS2ZEWFIU7OE33LCPHWS/graph.json","fetch_events":"https://pith.science/api/pith-number/ICJXTUFS2ZEWFIU7OE33LCPHWS/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS/action/storage_attestation","attest_author":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS/action/author_attestation","sign_citation":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS/action/citation_signature","submit_replication":"https://pith.science/pith/ICJXTUFS2ZEWFIU7OE33LCPHWS/action/replication_record"}},"created_at":"2026-05-18T02:08:15.529835+00:00","updated_at":"2026-05-18T02:08:15.529835+00:00"}