{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2012:Y3BGNZO7GGD5I4Q3BWYOVG3QJV","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"51d18843d858c50bd4661b25eac00406b8ff72f2f19248963af8b5788cb4f60a","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-14T13:33:03Z","title_canon_sha256":"52fc652521abc9eaf48ca9694f226feb71d2557c2bb5b1f5b29c025ba14bc3b0"},"schema_version":"1.0","source":{"id":"1211.3301","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1211.3301","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"arxiv_version","alias_value":"1211.3301v2","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1211.3301","created_at":"2026-05-18T02:56:52Z"},{"alias_kind":"pith_short_12","alias_value":"Y3BGNZO7GGD5","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_16","alias_value":"Y3BGNZO7GGD5I4Q3","created_at":"2026-05-18T12:27:27Z"},{"alias_kind":"pith_short_8","alias_value":"Y3BGNZO7","created_at":"2026-05-18T12:27:27Z"}],"graph_snapshots":[{"event_id":"sha256:6dffc626948ba466fe2926e8a7df46ca8f9e5dda46e7e5bb8c328055bd97d46d","target":"graph","created_at":"2026-05-18T02:56:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Let $X_1,X_2,...$ be independent identically distributed random variables with $\\mathbb E X_k=0$, $\\mathrm{Var} X_k=1$. Suppose that $\\varphi(t):=\\log \\mathbb E e^{t X_k}<\\infty$ for all $t>-\\sigma_0$ and some $\\sigma_0>0$. Let $S_k=X_1+...+X_k$ and $S_0=0$. We are interested in the limiting distribution of the multiscale scan statistic $$ M_n=\\max_{0\\leq i <j\\leq n} \\frac{S_j-S_i}{\\sqrt{j-i}}. $$ We prove that for an appropriate normalizing sequence $a_n$, the random variable $M_n^2-a_n$ converges to the Gumbel extreme-value law $\\exp\\{-e^{-c x}\\}$. The behavior of $M_n$ depends strongly on t","authors_text":"Yizao Wang, Zakhar Kabluchko","cross_cats":["math.ST","stat.TH"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-14T13:33:03Z","title":"Limiting distribution for the maximal standardized increment of a random walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1211.3301","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2d6aaa4ba276bec8f7f57fb2c933a38a6aaf57566b223309665e90a77880b1c0","target":"record","created_at":"2026-05-18T02:56:52Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"51d18843d858c50bd4661b25eac00406b8ff72f2f19248963af8b5788cb4f60a","cross_cats_sorted":["math.ST","stat.TH"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-11-14T13:33:03Z","title_canon_sha256":"52fc652521abc9eaf48ca9694f226feb71d2557c2bb5b1f5b29c025ba14bc3b0"},"schema_version":"1.0","source":{"id":"1211.3301","kind":"arxiv","version":2}},"canonical_sha256":"c6c266e5df3187d4721b0db0ea9b704d6e2ca9214016f46f5d29e25528935bd6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"c6c266e5df3187d4721b0db0ea9b704d6e2ca9214016f46f5d29e25528935bd6","first_computed_at":"2026-05-18T02:56:52.158926Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:56:52.158926Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"DmiNmsZDY3/ruMvfhvI6mbPuaf+wz27PzeYOq8dacP0Zios+AEshUPnnn5MLuP/LlfemEPC9noNk2zaa+53DCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:56:52.159357Z","signed_message":"canonical_sha256_bytes"},"source_id":"1211.3301","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2d6aaa4ba276bec8f7f57fb2c933a38a6aaf57566b223309665e90a77880b1c0","sha256:6dffc626948ba466fe2926e8a7df46ca8f9e5dda46e7e5bb8c328055bd97d46d"],"state_sha256":"e632bee3c6132757c62931f63ac11f8463d044f76c42e9341d25420f9a4bca02"}