{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2011:7YLBCFMO72F4TQMPROY5HPTB6X","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":"1963aee997e7a27945443fe243dfef31096d1cd90f16fc55c9395834df86bd5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-17T17:22:59Z","title_canon_sha256":"66d9d5d8fe48deea5b1cc6396313f61e41aea02bd8aba0e691a0ba62cbcc3fea"},"schema_version":"1.0","source":{"id":"1111.4159","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1111.4159","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"arxiv_version","alias_value":"1111.4159v3","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1111.4159","created_at":"2026-05-18T03:36:48Z"},{"alias_kind":"pith_short_12","alias_value":"7YLBCFMO72F4","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_16","alias_value":"7YLBCFMO72F4TQMP","created_at":"2026-05-18T12:26:22Z"},{"alias_kind":"pith_short_8","alias_value":"7YLBCFMO","created_at":"2026-05-18T12:26:22Z"}],"graph_snapshots":[{"event_id":"sha256:e92090c62d911cc11f31572e60df952aaaa08658eeeca8a5bdcf1e30e3910130","target":"graph","created_at":"2026-05-18T03:36:48Z","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 $(\\xi_1,\\eta_1),(\\xi_2,\\eta_2),...$ be a sequence of i.i.d.\\ copies of a random vector $(\\xi,\\eta)$ taking values in $\\R^2$, and let $S_n := \\xi_1+...+\\xi_n$. The sequence $(S_{n-1} + \\eta_n)_{n \\geq 1}$ is then called perturbed random walk.\n  We study random quantities defined in terms of the perturbed random walk: $\\tau(x)$, the first time the perturbed random walk exits the interval $(-\\infty,x]$, $N(x)$, the number of visits to the interval $(-\\infty,x]$, and $\\rho(x)$, the last time the perturbed random walk visits the interval $(-\\infty,x]$. We provide criteria for the a.s.\\ finitene","authors_text":"Alexander Iksanov, Gerold Alsmeyer, Matthias Meiners","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-17T17:22:59Z","title":"Power and exponential moments of the number of visits and related quantities for perturbed random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.4159","kind":"arxiv","version":3},"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":"sha256:091571c62e0e0a0f04349afc243ef8a7cd7aa7bf0cd4e12a2142ae21a18d5fca","target":"record","created_at":"2026-05-18T03:36:48Z","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":"1963aee997e7a27945443fe243dfef31096d1cd90f16fc55c9395834df86bd5d","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-11-17T17:22:59Z","title_canon_sha256":"66d9d5d8fe48deea5b1cc6396313f61e41aea02bd8aba0e691a0ba62cbcc3fea"},"schema_version":"1.0","source":{"id":"1111.4159","kind":"arxiv","version":3}},"canonical_sha256":"fe1611158efe8bc9c18f8bb1d3be61f5f14d94e0310993db4b99451327228dbe","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"fe1611158efe8bc9c18f8bb1d3be61f5f14d94e0310993db4b99451327228dbe","first_computed_at":"2026-05-18T03:36:48.186937Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:36:48.186937Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"WQ0yNVRSRf/yraw8VD588cHgQSUo87g3Tj2XCjS2sGfbvdPmd0pOgYoddsm5cvok92Zja2VSfU4BcX7bfhrdAA==","signature_status":"signed_v1","signed_at":"2026-05-18T03:36:48.187634Z","signed_message":"canonical_sha256_bytes"},"source_id":"1111.4159","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:091571c62e0e0a0f04349afc243ef8a7cd7aa7bf0cd4e12a2142ae21a18d5fca","sha256:e92090c62d911cc11f31572e60df952aaaa08658eeeca8a5bdcf1e30e3910130"],"state_sha256":"43d99a821e37f399651fc4aa9b35bc3dc400cdd68ced88db4f497c9ddc15abcd"}