{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:P6LJFC4CLIM2DCTWMTTCHTSYAR","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":"a9b5b8dfb55c50ba20449f0f3468e3583a4a7ac97f01e6448371ea1554e10fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-19T15:27:29Z","title_canon_sha256":"067852ce82fe617e383a6f7f295fc974e05d09a49cd16abdd268da6460b180ca"},"schema_version":"1.0","source":{"id":"1402.4698","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1402.4698","created_at":"2026-05-18T02:58:33Z"},{"alias_kind":"arxiv_version","alias_value":"1402.4698v1","created_at":"2026-05-18T02:58:33Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1402.4698","created_at":"2026-05-18T02:58:33Z"},{"alias_kind":"pith_short_12","alias_value":"P6LJFC4CLIM2","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_16","alias_value":"P6LJFC4CLIM2DCTW","created_at":"2026-05-18T12:28:43Z"},{"alias_kind":"pith_short_8","alias_value":"P6LJFC4C","created_at":"2026-05-18T12:28:43Z"}],"graph_snapshots":[{"event_id":"sha256:e39bede4e516fe10289a18165dd81ed368dad67362f13eed6332f33397424947","target":"graph","created_at":"2026-05-18T02:58:33Z","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 $(\\xi_k)$ and $(\\eta_k)$ be infinite independent samples from different distributions. We prove a functional limit theorem for the maximum of a perturbed random walk $\\underset{0\\leq k\\leq n}{\\max}\\,(\\xi_1+\\ldots+\\xi_k+\\eta_{k+1})$ in a situation where its asymptotics is affected by both $\\underset{0\\leq k\\leq n}{\\max}\\,(\\xi_1+\\ldots+\\xi_k)$ and $\\underset{1\\leq k\\leq n}{\\max}\\,\\eta_k$ to a comparable extent. This solves an open problem that we learned from the paper \"Renorming divergent perpetuities\" by P. Hitczenko and J. Weso{\\l}owski.","authors_text":"Alexander Iksanov, Andrey Pilipenko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-19T15:27:29Z","title":"A remark on the paper \"Renorming divergent perpetuities\""},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1402.4698","kind":"arxiv","version":1},"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":"sha256:79516baf89734c87bc491db3023daaf45f55258b32bfee08171e4affdcc91d3a","target":"record","created_at":"2026-05-18T02:58:33Z","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":"a9b5b8dfb55c50ba20449f0f3468e3583a4a7ac97f01e6448371ea1554e10fee","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-02-19T15:27:29Z","title_canon_sha256":"067852ce82fe617e383a6f7f295fc974e05d09a49cd16abdd268da6460b180ca"},"schema_version":"1.0","source":{"id":"1402.4698","kind":"arxiv","version":1}},"canonical_sha256":"7f96928b825a19a18a7664e623ce5804661dbcf9925dca7746b4b3dda2ff4c89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"7f96928b825a19a18a7664e623ce5804661dbcf9925dca7746b4b3dda2ff4c89","first_computed_at":"2026-05-18T02:58:33.431249Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:58:33.431249Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"tVnLF0cl+ldKXBG+ddSsETw2ynMlIkoO8Wz3OwAXp9CK05bLUNp1DF1bUw2m3SgIpwNZCbs/w2V5MN67BN4QAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:58:33.432087Z","signed_message":"canonical_sha256_bytes"},"source_id":"1402.4698","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:79516baf89734c87bc491db3023daaf45f55258b32bfee08171e4affdcc91d3a","sha256:e39bede4e516fe10289a18165dd81ed368dad67362f13eed6332f33397424947"],"state_sha256":"dee86f947fde76138f88ae33d47d75021e7a21706d58df06ecfb0703ba76e235"}