{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:C2IB3CB5PYLPDRD63UBF3BNCNI","short_pith_number":"pith:C2IB3CB5","schema_version":"1.0","canonical_sha256":"16901d883d7e16f1c47edd025d85a26a28d813428e8e838abfcf4a84d8589b58","source":{"kind":"arxiv","id":"1307.3583","version":3},"attestation_state":"computed","paper":{"title":"Slowdown in branching Brownian motion with inhomogeneous variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ofer Zeitouni, Pascal Maillard","submitted_at":"2013-07-12T21:23:56Z","abstract_excerpt":"We consider a model of Branching Brownian Motion with time-inhomogeneous variance of the form \\sigma(t/T), where \\sigma is a strictly decreasing function. Fang and Zeitouni (2012) showed that the maximal particle's position M_T is such that M_T-v_\\sigma T is negative of order T^{-1/3}, where v_\\sigma is the integral of the function \\sigma over the interval [0,1]. In this paper, we refine we refine this result and show the existence of a function m_T, such that M_T-m_T converges in law, as T\\to\\infty. Furthermore, m_T=v_\\sigma T - w_\\sigma T^{1/3} - \\sigma(1)\\log T + O(1) with w_\\sigma = 2^{-1/"},"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":"1307.3583","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-07-12T21:23:56Z","cross_cats_sorted":[],"title_canon_sha256":"063448ea0b26b9db33ef5cca50f90296610491759cc5417492cdf7e84df6ad5c","abstract_canon_sha256":"9ca5b8276113b65d9965d98d11ebb59ae2b46499c0f3bec2b06245fb27daa024"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:12:57.382881Z","signature_b64":"WEXE7ahmzC6+hm3ZeBYr2W0Cz3FSIp1D60i7IeKWwnh7lwCKrcdUw4hmYm04h/uvMmlqXFa0dglyHt7SLtgvBw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"16901d883d7e16f1c47edd025d85a26a28d813428e8e838abfcf4a84d8589b58","last_reissued_at":"2026-05-18T00:12:57.382225Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:12:57.382225Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Slowdown in branching Brownian motion with inhomogeneous variance","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ofer Zeitouni, Pascal Maillard","submitted_at":"2013-07-12T21:23:56Z","abstract_excerpt":"We consider a model of Branching Brownian Motion with time-inhomogeneous variance of the form \\sigma(t/T), where \\sigma is a strictly decreasing function. Fang and Zeitouni (2012) showed that the maximal particle's position M_T is such that M_T-v_\\sigma T is negative of order T^{-1/3}, where v_\\sigma is the integral of the function \\sigma over the interval [0,1]. In this paper, we refine we refine this result and show the existence of a function m_T, such that M_T-m_T converges in law, as T\\to\\infty. Furthermore, m_T=v_\\sigma T - w_\\sigma T^{1/3} - \\sigma(1)\\log T + O(1) with w_\\sigma = 2^{-1/"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1307.3583","kind":"arxiv","version":3},"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":"1307.3583","created_at":"2026-05-18T00:12:57.382332+00:00"},{"alias_kind":"arxiv_version","alias_value":"1307.3583v3","created_at":"2026-05-18T00:12:57.382332+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1307.3583","created_at":"2026-05-18T00:12:57.382332+00:00"},{"alias_kind":"pith_short_12","alias_value":"C2IB3CB5PYLP","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_16","alias_value":"C2IB3CB5PYLPDRD6","created_at":"2026-05-18T12:27:40.988391+00:00"},{"alias_kind":"pith_short_8","alias_value":"C2IB3CB5","created_at":"2026-05-18T12:27:40.988391+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/C2IB3CB5PYLPDRD63UBF3BNCNI","json":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI.json","graph_json":"https://pith.science/api/pith-number/C2IB3CB5PYLPDRD63UBF3BNCNI/graph.json","events_json":"https://pith.science/api/pith-number/C2IB3CB5PYLPDRD63UBF3BNCNI/events.json","paper":"https://pith.science/paper/C2IB3CB5"},"agent_actions":{"view_html":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI","download_json":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI.json","view_paper":"https://pith.science/paper/C2IB3CB5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1307.3583&json=true","fetch_graph":"https://pith.science/api/pith-number/C2IB3CB5PYLPDRD63UBF3BNCNI/graph.json","fetch_events":"https://pith.science/api/pith-number/C2IB3CB5PYLPDRD63UBF3BNCNI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI/action/storage_attestation","attest_author":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI/action/author_attestation","sign_citation":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI/action/citation_signature","submit_replication":"https://pith.science/pith/C2IB3CB5PYLPDRD63UBF3BNCNI/action/replication_record"}},"created_at":"2026-05-18T00:12:57.382332+00:00","updated_at":"2026-05-18T00:12:57.382332+00:00"}