{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:H2BXCAIECEVTEAEWTZL2FZD34R","short_pith_number":"pith:H2BXCAIE","schema_version":"1.0","canonical_sha256":"3e83710104112b3200969e57a2e47be46bb39a69e9b4502a8dcb8060314b6d75","source":{"kind":"arxiv","id":"1304.7569","version":4},"attestation_state":"computed","paper":{"title":"First order global asymptotics for confined particles with singular pair repulsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Djalil Chafa\\\"i (CEREMADE, IUF), LAMA, Nathael Gozlan (LAMA), Pierre-Andr\\'e Zitt (LAMA)","submitted_at":"2013-04-29T05:33:24Z","abstract_excerpt":"We study a physical system of $N$ interacting particles in $\\mathbb{R}^d$, $d\\geq1$, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution as $N$ tends to infinity. In the case of Riesz interaction, including Coulomb interaction in arbitrary dimension $d>2$, the rate function is strictly convex and admits a unique minimum, the equilibrium measure, characterized via its potential. It follows that almost surely, the empirical distribution of the particles tends to this equilibrium measure as $N$ tends to infinity. "},"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":"1304.7569","kind":"arxiv","version":4},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-04-29T05:33:24Z","cross_cats_sorted":["math-ph","math.CA","math.MP"],"title_canon_sha256":"e041d7726c85d22169024d13a6d5d72dc54412bc7bf86bc629d9d59e84cbebb8","abstract_canon_sha256":"4516ea758eca4466a8c325fe91e17084fb775af361ba3b6024f1ac09e173f923"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:43:24.413846Z","signature_b64":"jrx7mLZqYm8zv04TpvuxHlwqj7lfC+6fcgAk6PlGw2CsanXC48AWPQtk3jPkbBx1at9KgYKmBA5NAxpbochyDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e83710104112b3200969e57a2e47be46bb39a69e9b4502a8dcb8060314b6d75","last_reissued_at":"2026-05-18T02:43:24.413226Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:43:24.413226Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"First order global asymptotics for confined particles with singular pair repulsion","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CA","math.MP"],"primary_cat":"math.PR","authors_text":"Djalil Chafa\\\"i (CEREMADE, IUF), LAMA, Nathael Gozlan (LAMA), Pierre-Andr\\'e Zitt (LAMA)","submitted_at":"2013-04-29T05:33:24Z","abstract_excerpt":"We study a physical system of $N$ interacting particles in $\\mathbb{R}^d$, $d\\geq1$, subject to pair repulsion and confined by an external field. We establish a large deviations principle for their empirical distribution as $N$ tends to infinity. In the case of Riesz interaction, including Coulomb interaction in arbitrary dimension $d>2$, the rate function is strictly convex and admits a unique minimum, the equilibrium measure, characterized via its potential. It follows that almost surely, the empirical distribution of the particles tends to this equilibrium measure as $N$ tends to infinity. "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7569","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":"1304.7569","created_at":"2026-05-18T02:43:24.413322+00:00"},{"alias_kind":"arxiv_version","alias_value":"1304.7569v4","created_at":"2026-05-18T02:43:24.413322+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1304.7569","created_at":"2026-05-18T02:43:24.413322+00:00"},{"alias_kind":"pith_short_12","alias_value":"H2BXCAIECEVT","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_16","alias_value":"H2BXCAIECEVTEAEW","created_at":"2026-05-18T12:27:46.883200+00:00"},{"alias_kind":"pith_short_8","alias_value":"H2BXCAIE","created_at":"2026-05-18T12:27:46.883200+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/H2BXCAIECEVTEAEWTZL2FZD34R","json":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R.json","graph_json":"https://pith.science/api/pith-number/H2BXCAIECEVTEAEWTZL2FZD34R/graph.json","events_json":"https://pith.science/api/pith-number/H2BXCAIECEVTEAEWTZL2FZD34R/events.json","paper":"https://pith.science/paper/H2BXCAIE"},"agent_actions":{"view_html":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R","download_json":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R.json","view_paper":"https://pith.science/paper/H2BXCAIE","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1304.7569&json=true","fetch_graph":"https://pith.science/api/pith-number/H2BXCAIECEVTEAEWTZL2FZD34R/graph.json","fetch_events":"https://pith.science/api/pith-number/H2BXCAIECEVTEAEWTZL2FZD34R/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R/action/timestamp_anchor","attest_storage":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R/action/storage_attestation","attest_author":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R/action/author_attestation","sign_citation":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R/action/citation_signature","submit_replication":"https://pith.science/pith/H2BXCAIECEVTEAEWTZL2FZD34R/action/replication_record"}},"created_at":"2026-05-18T02:43:24.413322+00:00","updated_at":"2026-05-18T02:43:24.413322+00:00"}