{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:LSVG6WL3S3HBMQYS4HLUZD6DUU","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":"28cc4f7b9711519540974d7dcc173d4037bcda41c1be9fb788a2496c6ff6f973","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-24T07:01:21Z","title_canon_sha256":"8599135f1de36fefb65e0c712055302752b49f9c0c076841b58d87c07e7fd255"},"schema_version":"1.0","source":{"id":"1301.5713","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1301.5713","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"arxiv_version","alias_value":"1301.5713v2","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1301.5713","created_at":"2026-05-18T03:05:28Z"},{"alias_kind":"pith_short_12","alias_value":"LSVG6WL3S3HB","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_16","alias_value":"LSVG6WL3S3HBMQYS","created_at":"2026-05-18T12:27:51Z"},{"alias_kind":"pith_short_8","alias_value":"LSVG6WL3","created_at":"2026-05-18T12:27:51Z"}],"graph_snapshots":[{"event_id":"sha256:43bb394ddca2d18bfd89a35fde88bea7879a6b58fb736406ecc5dd324f892375","target":"graph","created_at":"2026-05-18T03:05:28Z","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":"In this article we refine well-known results concerning the fluctuations of one-dimensional random walks. More precisely, if $(S_n)_{n \\geq 0}$ is a random walk starting from 0 and $r\\geq 0$, we obtain the precise asymptotic behavior as $n\\to\\infty$ of $\\mathbb P[\\tau^{>r}=n, S_n\\in K]$ and $\\mathbb P[\\tau^{>r}>n, S_n\\in K]$, where $\\tau^{>r}$ is the first time that the random walk reaches the set $]r,\\infty[$, and $K$ is a compact set. Our assumptions on the jumps of the random walks are optimal. Our results give an answer to a question of Lalley stated in [9], and are applied to obtain the a","authors_text":"Kilian Raschel, Marc Peign\\'e, Rim Essifi","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-24T07:01:21Z","title":"Some aspects of fluctuations of random walks on R and applications to random walks on R+ with non-elastic reflection at 0"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.5713","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":"sha256:9e38c9420118ff50db16402b88c7724efc8b42f4b8879dfa2ab0e6fce4e5be60","target":"record","created_at":"2026-05-18T03:05:28Z","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":"28cc4f7b9711519540974d7dcc173d4037bcda41c1be9fb788a2496c6ff6f973","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-01-24T07:01:21Z","title_canon_sha256":"8599135f1de36fefb65e0c712055302752b49f9c0c076841b58d87c07e7fd255"},"schema_version":"1.0","source":{"id":"1301.5713","kind":"arxiv","version":2}},"canonical_sha256":"5caa6f597b96ce164312e1d74c8fc3a5139acf662b881361459d1cf8b798fcc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"5caa6f597b96ce164312e1d74c8fc3a5139acf662b881361459d1cf8b798fcc6","first_computed_at":"2026-05-18T03:05:28.252167Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:05:28.252167Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"p1VKLTQBE8Sz15bsgjeblMH8W9LYEfMHTJZQSFRX6xeC/gDTvsvVN0f+drAK0U0magaF5E5ovP2e8t0h6IjsAw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:05:28.252690Z","signed_message":"canonical_sha256_bytes"},"source_id":"1301.5713","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:9e38c9420118ff50db16402b88c7724efc8b42f4b8879dfa2ab0e6fce4e5be60","sha256:43bb394ddca2d18bfd89a35fde88bea7879a6b58fb736406ecc5dd324f892375"],"state_sha256":"a2db1c514850b5d1169d3e3f4caee3393b40b2e271b82bd1fdf5eddb3f56a37b"}