{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:OVI44GOYAQKCMDKM767MEZC77D","short_pith_number":"pith:OVI44GOY","schema_version":"1.0","canonical_sha256":"7551ce19d80414260d4cffbec2645ff8f1c7c990910070d04e12e4d586ac810b","source":{"kind":"arxiv","id":"1504.02829","version":2},"attestation_state":"computed","paper":{"title":"Poincar\\'e Inequality for Dirichlet Distributions and Infinite-Dimensional Generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F.-Y. Wang, L. Miclo, S. Feng","submitted_at":"2015-04-11T03:50:00Z","abstract_excerpt":"For any $N\\ge 2$ and $\\aa:=(\\aa_1,\\cdots, \\aa_{N+1})\\in (0,\\infty)^{N+1}$, let $\\mu^{(N)}_{\\aa}$ be the corresponding Dirichlet distribution on $\\DD:= \\big\\{ x=(x_i)_{1\\le i\\le N}\\in [0,1]^N:\\ \\sum_{1\\le i\\le N} x_i\\le 1\\big\\}.$ We prove the Poincar\\'e inequality\n  $$\\mu^{(N)}_{\\aa}(f^2)\\le \\ff 1 {\\aa_{N+1}} \\int_{\\DD}\\Big\\{\\Big(1-\\sum_{1\\le i\\le N} x_i\\Big) \\sum_{n=1}^N x_n(\\pp_n f)^2\\Big\\}\\mu^{(N)}_\\aa(\\d x)+\\mu^{(N)}_{\\aa}(f)^2,\\ f\\in C^1(\\DD)$$ and show that the constant $\\ff 1 {\\aa_{N+1}}$ is sharp.\n  Consequently, the associated diffusion process on $\\DD$ converges to $\\mu^{(N)}_{\\aa}$ i"},"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":"1504.02829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-04-11T03:50:00Z","cross_cats_sorted":[],"title_canon_sha256":"14d3fb1d8f4cd1c07f73b6a644148858461484ee9d8209fe94a15a105bb161ab","abstract_canon_sha256":"79591a6f3fbc9b0496f4937497ec87b8cb1575d0069e73612e91aa7a4f244bdc"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:33:58.394372Z","signature_b64":"TMVctHiXAjmTegQACuah+6qzbDnn1YqW1+Q6TPAfo94qUzo4Qp/fsDjIJwapfEGYLkL+q4eeffd7emqwNoZcBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7551ce19d80414260d4cffbec2645ff8f1c7c990910070d04e12e4d586ac810b","last_reissued_at":"2026-05-18T01:33:58.393963Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:33:58.393963Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Poincar\\'e Inequality for Dirichlet Distributions and Infinite-Dimensional Generalizations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"F.-Y. Wang, L. Miclo, S. Feng","submitted_at":"2015-04-11T03:50:00Z","abstract_excerpt":"For any $N\\ge 2$ and $\\aa:=(\\aa_1,\\cdots, \\aa_{N+1})\\in (0,\\infty)^{N+1}$, let $\\mu^{(N)}_{\\aa}$ be the corresponding Dirichlet distribution on $\\DD:= \\big\\{ x=(x_i)_{1\\le i\\le N}\\in [0,1]^N:\\ \\sum_{1\\le i\\le N} x_i\\le 1\\big\\}.$ We prove the Poincar\\'e inequality\n  $$\\mu^{(N)}_{\\aa}(f^2)\\le \\ff 1 {\\aa_{N+1}} \\int_{\\DD}\\Big\\{\\Big(1-\\sum_{1\\le i\\le N} x_i\\Big) \\sum_{n=1}^N x_n(\\pp_n f)^2\\Big\\}\\mu^{(N)}_\\aa(\\d x)+\\mu^{(N)}_{\\aa}(f)^2,\\ f\\in C^1(\\DD)$$ and show that the constant $\\ff 1 {\\aa_{N+1}}$ is sharp.\n  Consequently, the associated diffusion process on $\\DD$ converges to $\\mu^{(N)}_{\\aa}$ i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.02829","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":"1504.02829","created_at":"2026-05-18T01:33:58.394021+00:00"},{"alias_kind":"arxiv_version","alias_value":"1504.02829v2","created_at":"2026-05-18T01:33:58.394021+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1504.02829","created_at":"2026-05-18T01:33:58.394021+00:00"},{"alias_kind":"pith_short_12","alias_value":"OVI44GOYAQKC","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_16","alias_value":"OVI44GOYAQKCMDKM","created_at":"2026-05-18T12:29:34.919912+00:00"},{"alias_kind":"pith_short_8","alias_value":"OVI44GOY","created_at":"2026-05-18T12:29:34.919912+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/OVI44GOYAQKCMDKM767MEZC77D","json":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D.json","graph_json":"https://pith.science/api/pith-number/OVI44GOYAQKCMDKM767MEZC77D/graph.json","events_json":"https://pith.science/api/pith-number/OVI44GOYAQKCMDKM767MEZC77D/events.json","paper":"https://pith.science/paper/OVI44GOY"},"agent_actions":{"view_html":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D","download_json":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D.json","view_paper":"https://pith.science/paper/OVI44GOY","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1504.02829&json=true","fetch_graph":"https://pith.science/api/pith-number/OVI44GOYAQKCMDKM767MEZC77D/graph.json","fetch_events":"https://pith.science/api/pith-number/OVI44GOYAQKCMDKM767MEZC77D/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D/action/timestamp_anchor","attest_storage":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D/action/storage_attestation","attest_author":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D/action/author_attestation","sign_citation":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D/action/citation_signature","submit_replication":"https://pith.science/pith/OVI44GOYAQKCMDKM767MEZC77D/action/replication_record"}},"created_at":"2026-05-18T01:33:58.394021+00:00","updated_at":"2026-05-18T01:33:58.394021+00:00"}