{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2014:MUI7IIPWWV6FKDUXMLHZLDVA76","short_pith_number":"pith:MUI7IIPW","schema_version":"1.0","canonical_sha256":"6511f421f6b57c550e9762cf958ea0ffb02ebe0fc91994334ed84c9cf2bb0a44","source":{"kind":"arxiv","id":"1404.1480","version":1},"attestation_state":"computed","paper":{"title":"Weak convergence of partial maxima processes in the $M_{1}$ topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Danijel Krizmani\\'c","submitted_at":"2014-04-05T13:58:05Z","abstract_excerpt":"It is known that for a sequence of independent and identically distributed random variables $(X_{n})$ the regular variation condition is equivalent to weak convergence of partial maxima $M_{n}= \\max\\{X_{1}, \\ldots, X_{n}\\}$, appropriately scaled. A functional version of this is known to be true as well, the limit process being an extremal process, and the convergence takes place in the space of c\\`{a}dl\\`{a}g functions endowed with the Skorohod $J_{1}$ topology. We first show that weak convergence of partial maxima $M_{n}$ holds also for a class of weakly dependent sequences under the joint re"},"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":"1404.1480","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-05T13:58:05Z","cross_cats_sorted":[],"title_canon_sha256":"72e2d7a9681dc24e4d18aecf461618c6dd7c2e1ca19c29afe18f45e31f50a8e2","abstract_canon_sha256":"52c2ea71ff9f01cf895c431460d7bcd39d992cf3e50841dc3644576563e4e817"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:54:46.180820Z","signature_b64":"pYhBI3eRSHXQwCY8OdeE8REfag9Aguiv6UmCQ6WrshgJriDeP9zpXqkobbjIl02lXY4BRFWylqSNFH58CBOaDw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6511f421f6b57c550e9762cf958ea0ffb02ebe0fc91994334ed84c9cf2bb0a44","last_reissued_at":"2026-05-18T02:54:46.180408Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:54:46.180408Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Weak convergence of partial maxima processes in the $M_{1}$ topology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Danijel Krizmani\\'c","submitted_at":"2014-04-05T13:58:05Z","abstract_excerpt":"It is known that for a sequence of independent and identically distributed random variables $(X_{n})$ the regular variation condition is equivalent to weak convergence of partial maxima $M_{n}= \\max\\{X_{1}, \\ldots, X_{n}\\}$, appropriately scaled. A functional version of this is known to be true as well, the limit process being an extremal process, and the convergence takes place in the space of c\\`{a}dl\\`{a}g functions endowed with the Skorohod $J_{1}$ topology. We first show that weak convergence of partial maxima $M_{n}$ holds also for a class of weakly dependent sequences under the joint re"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.1480","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":"1404.1480","created_at":"2026-05-18T02:54:46.180475+00:00"},{"alias_kind":"arxiv_version","alias_value":"1404.1480v1","created_at":"2026-05-18T02:54:46.180475+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.1480","created_at":"2026-05-18T02:54:46.180475+00:00"},{"alias_kind":"pith_short_12","alias_value":"MUI7IIPWWV6F","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_16","alias_value":"MUI7IIPWWV6FKDUX","created_at":"2026-05-18T12:28:38.356838+00:00"},{"alias_kind":"pith_short_8","alias_value":"MUI7IIPW","created_at":"2026-05-18T12:28:38.356838+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/MUI7IIPWWV6FKDUXMLHZLDVA76","json":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76.json","graph_json":"https://pith.science/api/pith-number/MUI7IIPWWV6FKDUXMLHZLDVA76/graph.json","events_json":"https://pith.science/api/pith-number/MUI7IIPWWV6FKDUXMLHZLDVA76/events.json","paper":"https://pith.science/paper/MUI7IIPW"},"agent_actions":{"view_html":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76","download_json":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76.json","view_paper":"https://pith.science/paper/MUI7IIPW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1404.1480&json=true","fetch_graph":"https://pith.science/api/pith-number/MUI7IIPWWV6FKDUXMLHZLDVA76/graph.json","fetch_events":"https://pith.science/api/pith-number/MUI7IIPWWV6FKDUXMLHZLDVA76/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76/action/storage_attestation","attest_author":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76/action/author_attestation","sign_citation":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76/action/citation_signature","submit_replication":"https://pith.science/pith/MUI7IIPWWV6FKDUXMLHZLDVA76/action/replication_record"}},"created_at":"2026-05-18T02:54:46.180475+00:00","updated_at":"2026-05-18T02:54:46.180475+00:00"}