{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2022:6QAAQUI4C4KAEWSIKTQYFQ46EM","short_pith_number":"pith:6QAAQUI4","schema_version":"1.0","canonical_sha256":"f40008511c1714025a4854e182c39e23047172878ecf28c65fd7d58c101c40b2","source":{"kind":"arxiv","id":"2211.08538","version":2},"attestation_state":"computed","paper":{"title":"Random Walks in the High-Dimensional Limit I: The Wiener Spiral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Zakhar Kabluchko","submitted_at":"2022-11-15T22:20:51Z","abstract_excerpt":"We prove limit theorems for random walks with $n$ steps in the $d$-dimensional Euclidean space as both $n$ and $d$ tend to infinity. One of our results states that the path of such a random walk, viewed as a compact subset of the infinite-dimensional Hilbert space $\\ell^2$, converges in probability in the Hausdorff distance up to isometry and also in the Gromov-Hausdorff sense to the Wiener spiral, as $d,n\\to\\infty$. Another group of results describes various possible limit distributions for the squared distance between the random walker at time $n$ and the origin."},"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":"2211.08538","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2022-11-15T22:20:51Z","cross_cats_sorted":[],"title_canon_sha256":"b71d8f16ce8d2d9975342002a422d057d76d8adcd42375ea21f6495ae02bdb52","abstract_canon_sha256":"dc16433f709298a8296835e30dc9ae384211009006f8132105fa10c6446f7ad6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-07-05T06:11:58.171237Z","signature_b64":"5U0lGEL1fUamfNYfCzWsC9iOew9Ox43AjkMYUyJVYhPilecrFRcaKKXm+AE7XreK8atMYaGvkyTmblVyqF6OCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f40008511c1714025a4854e182c39e23047172878ecf28c65fd7d58c101c40b2","last_reissued_at":"2026-07-05T06:11:58.170764Z","signature_status":"signed_v1","first_computed_at":"2026-07-05T06:11:58.170764Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Random Walks in the High-Dimensional Limit I: The Wiener Spiral","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Marynych, Zakhar Kabluchko","submitted_at":"2022-11-15T22:20:51Z","abstract_excerpt":"We prove limit theorems for random walks with $n$ steps in the $d$-dimensional Euclidean space as both $n$ and $d$ tend to infinity. One of our results states that the path of such a random walk, viewed as a compact subset of the infinite-dimensional Hilbert space $\\ell^2$, converges in probability in the Hausdorff distance up to isometry and also in the Gromov-Hausdorff sense to the Wiener spiral, as $d,n\\to\\infty$. Another group of results describes various possible limit distributions for the squared distance between the random walker at time $n$ and the origin."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2211.08538","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2211.08538/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"2211.08538","created_at":"2026-07-05T06:11:58.170830+00:00"},{"alias_kind":"arxiv_version","alias_value":"2211.08538v2","created_at":"2026-07-05T06:11:58.170830+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2211.08538","created_at":"2026-07-05T06:11:58.170830+00:00"},{"alias_kind":"pith_short_12","alias_value":"6QAAQUI4C4KA","created_at":"2026-07-05T06:11:58.170830+00:00"},{"alias_kind":"pith_short_16","alias_value":"6QAAQUI4C4KAEWSI","created_at":"2026-07-05T06:11:58.170830+00:00"},{"alias_kind":"pith_short_8","alias_value":"6QAAQUI4","created_at":"2026-07-05T06:11:58.170830+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"2411.17023","citing_title":"On the first hitting time of a high-dimensional orthant","ref_index":15,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM","json":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM.json","graph_json":"https://pith.science/api/pith-number/6QAAQUI4C4KAEWSIKTQYFQ46EM/graph.json","events_json":"https://pith.science/api/pith-number/6QAAQUI4C4KAEWSIKTQYFQ46EM/events.json","paper":"https://pith.science/paper/6QAAQUI4"},"agent_actions":{"view_html":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM","download_json":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM.json","view_paper":"https://pith.science/paper/6QAAQUI4","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=2211.08538&json=true","fetch_graph":"https://pith.science/api/pith-number/6QAAQUI4C4KAEWSIKTQYFQ46EM/graph.json","fetch_events":"https://pith.science/api/pith-number/6QAAQUI4C4KAEWSIKTQYFQ46EM/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM/action/storage_attestation","attest_author":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM/action/author_attestation","sign_citation":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM/action/citation_signature","submit_replication":"https://pith.science/pith/6QAAQUI4C4KAEWSIKTQYFQ46EM/action/replication_record"}},"created_at":"2026-07-05T06:11:58.170830+00:00","updated_at":"2026-07-05T06:11:58.170830+00:00"}