{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:FZBSRZ6B52XVCAVHOOL52C7G5C","short_pith_number":"pith:FZBSRZ6B","schema_version":"1.0","canonical_sha256":"2e4328e7c1eeaf5102a77397dd0be6e8aaa2de40a1ce0cbd22a844bda2d1dea1","source":{"kind":"arxiv","id":"1810.06275","version":1},"attestation_state":"computed","paper":{"title":"Functional limit theorems for random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chak Hei Lo, Clare Wallace, James McRedmond","submitted_at":"2018-10-15T11:15:14Z","abstract_excerpt":"We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's theorem). For the latter, we survey the underlying weak convergence theory, drawing heavily on the exposition of Billingsley, but explicitly treat the multidimensional case.\n  Our two main applications are to the convex hull of a random walk and the centre of mass process associated to a random walk. In particular, we establish the limit sets of the convex hull in t"},"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":"1810.06275","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-10-15T11:15:14Z","cross_cats_sorted":[],"title_canon_sha256":"2f7ddd7f5ffe69b1f64e4e410c96151a45c56610440144c09978e0542314c98e","abstract_canon_sha256":"5f0462d370888439db77a0deebb5ab6a0c7ec24f3097491695dc559bb986fe9c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:03:20.943468Z","signature_b64":"D+Q/eWbWFSNMNKYBAM9va4LVwh6+4XZnvu8eJfaGn+jDoG8vPaDyf2qjQa+IsRIVO5nAa3gGuIo0QXl9tc4/Aw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2e4328e7c1eeaf5102a77397dd0be6e8aaa2de40a1ce0cbd22a844bda2d1dea1","last_reissued_at":"2026-05-18T00:03:20.943029Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:03:20.943029Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Functional limit theorems for random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Chak Hei Lo, Clare Wallace, James McRedmond","submitted_at":"2018-10-15T11:15:14Z","abstract_excerpt":"We survey some geometrical properties of trajectories of $d$-dimensional random walks via the application of functional limit theorems. We focus on the functional law of large numbers and functional central limit theorem (Donsker's theorem). For the latter, we survey the underlying weak convergence theory, drawing heavily on the exposition of Billingsley, but explicitly treat the multidimensional case.\n  Our two main applications are to the convex hull of a random walk and the centre of mass process associated to a random walk. In particular, we establish the limit sets of the convex hull in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.06275","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":"1810.06275","created_at":"2026-05-18T00:03:20.943087+00:00"},{"alias_kind":"arxiv_version","alias_value":"1810.06275v1","created_at":"2026-05-18T00:03:20.943087+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1810.06275","created_at":"2026-05-18T00:03:20.943087+00:00"},{"alias_kind":"pith_short_12","alias_value":"FZBSRZ6B52XV","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_16","alias_value":"FZBSRZ6B52XVCAVH","created_at":"2026-05-18T12:32:25.280505+00:00"},{"alias_kind":"pith_short_8","alias_value":"FZBSRZ6B","created_at":"2026-05-18T12:32:25.280505+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/FZBSRZ6B52XVCAVHOOL52C7G5C","json":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C.json","graph_json":"https://pith.science/api/pith-number/FZBSRZ6B52XVCAVHOOL52C7G5C/graph.json","events_json":"https://pith.science/api/pith-number/FZBSRZ6B52XVCAVHOOL52C7G5C/events.json","paper":"https://pith.science/paper/FZBSRZ6B"},"agent_actions":{"view_html":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C","download_json":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C.json","view_paper":"https://pith.science/paper/FZBSRZ6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1810.06275&json=true","fetch_graph":"https://pith.science/api/pith-number/FZBSRZ6B52XVCAVHOOL52C7G5C/graph.json","fetch_events":"https://pith.science/api/pith-number/FZBSRZ6B52XVCAVHOOL52C7G5C/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C/action/timestamp_anchor","attest_storage":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C/action/storage_attestation","attest_author":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C/action/author_attestation","sign_citation":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C/action/citation_signature","submit_replication":"https://pith.science/pith/FZBSRZ6B52XVCAVHOOL52C7G5C/action/replication_record"}},"created_at":"2026-05-18T00:03:20.943087+00:00","updated_at":"2026-05-18T00:03:20.943087+00:00"}