{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:2HJQPYDYZOEFQCGPPEH3KSNWQR","short_pith_number":"pith:2HJQPYDY","schema_version":"1.0","canonical_sha256":"d1d307e078cb885808cf790fb549b684573a3634cd0563c8aa883253489fd3fa","source":{"kind":"arxiv","id":"1710.11328","version":2},"attestation_state":"computed","paper":{"title":"Gaussian Approximation of the Distribution of Strongly Repelling Particles on the Unit Circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexander Soshnikov, Yuanyuan Xu","submitted_at":"2017-10-31T05:12:08Z","abstract_excerpt":"In this paper, we consider a strongly-repelling model of $n$ ordered particles $\\{e^{i \\theta_j}\\}_{j=0}^{n-1}$ with the density $p({\\theta_0},\\cdots, \\theta_{n-1})=\\frac{1}{Z_n} \\exp \\left\\{-\\frac{\\beta}{2}\\sum_{j \\neq k} \\sin^{-2} \\left( \\frac{\\theta_j-\\theta_k}{2}\\right)\\right\\}$, $\\beta>0$. Let $\\theta_j=\\frac{2 \\pi j}{n}+\\frac{x_j}{n^2}+const$ such that $\\sum_{j=0}^{n-1}x_j=0$. Define $\\zeta_n \\left( \\frac{2 \\pi j}{n}\\right) =\\frac{x_j}{\\sqrt{n}}$ and extend $\\zeta_n$ piecewise linearly to $[0, 2 \\pi]$. We prove the functional convergence of $\\zeta_n(t)$ to $\\zeta(t)=\\sqrt{\\frac{2}{\\beta}"},"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":"1710.11328","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-10-31T05:12:08Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"e9e758152a465e5631ba4649bacedeefb17ce528392a2b747765e66bb85ba775","abstract_canon_sha256":"c6e43b05e0af65ee8ff448e6ac8d860e85cbec338d0675f7c55e36923449a237"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:47.092688Z","signature_b64":"ZPvQK7ExsG5hyfij4Y+phRKrpgWNrQbwH4JgIk1X2fmDYcXCQnA2Cv6zd75WLVfztUKeqw84ovo6Lly14O6+DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d1d307e078cb885808cf790fb549b684573a3634cd0563c8aa883253489fd3fa","last_reissued_at":"2026-05-18T00:14:47.092087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:47.092087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gaussian Approximation of the Distribution of Strongly Repelling Particles on the Unit Circle","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.PR","authors_text":"Alexander Soshnikov, Yuanyuan Xu","submitted_at":"2017-10-31T05:12:08Z","abstract_excerpt":"In this paper, we consider a strongly-repelling model of $n$ ordered particles $\\{e^{i \\theta_j}\\}_{j=0}^{n-1}$ with the density $p({\\theta_0},\\cdots, \\theta_{n-1})=\\frac{1}{Z_n} \\exp \\left\\{-\\frac{\\beta}{2}\\sum_{j \\neq k} \\sin^{-2} \\left( \\frac{\\theta_j-\\theta_k}{2}\\right)\\right\\}$, $\\beta>0$. Let $\\theta_j=\\frac{2 \\pi j}{n}+\\frac{x_j}{n^2}+const$ such that $\\sum_{j=0}^{n-1}x_j=0$. Define $\\zeta_n \\left( \\frac{2 \\pi j}{n}\\right) =\\frac{x_j}{\\sqrt{n}}$ and extend $\\zeta_n$ piecewise linearly to $[0, 2 \\pi]$. We prove the functional convergence of $\\zeta_n(t)$ to $\\zeta(t)=\\sqrt{\\frac{2}{\\beta}"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.11328","kind":"arxiv","version":2},"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":"1710.11328","created_at":"2026-05-18T00:14:47.092162+00:00"},{"alias_kind":"arxiv_version","alias_value":"1710.11328v2","created_at":"2026-05-18T00:14:47.092162+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.11328","created_at":"2026-05-18T00:14:47.092162+00:00"},{"alias_kind":"pith_short_12","alias_value":"2HJQPYDYZOEF","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_16","alias_value":"2HJQPYDYZOEFQCGP","created_at":"2026-05-18T12:30:55.937587+00:00"},{"alias_kind":"pith_short_8","alias_value":"2HJQPYDY","created_at":"2026-05-18T12:30:55.937587+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/2HJQPYDYZOEFQCGPPEH3KSNWQR","json":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR.json","graph_json":"https://pith.science/api/pith-number/2HJQPYDYZOEFQCGPPEH3KSNWQR/graph.json","events_json":"https://pith.science/api/pith-number/2HJQPYDYZOEFQCGPPEH3KSNWQR/events.json","paper":"https://pith.science/paper/2HJQPYDY"},"agent_actions":{"view_html":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR","download_json":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR.json","view_paper":"https://pith.science/paper/2HJQPYDY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1710.11328&json=true","fetch_graph":"https://pith.science/api/pith-number/2HJQPYDYZOEFQCGPPEH3KSNWQR/graph.json","fetch_events":"https://pith.science/api/pith-number/2HJQPYDYZOEFQCGPPEH3KSNWQR/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR/action/storage_attestation","attest_author":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR/action/author_attestation","sign_citation":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR/action/citation_signature","submit_replication":"https://pith.science/pith/2HJQPYDYZOEFQCGPPEH3KSNWQR/action/replication_record"}},"created_at":"2026-05-18T00:14:47.092162+00:00","updated_at":"2026-05-18T00:14:47.092162+00:00"}