{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2013:ZQ6BZXT53QFXGGO42QOCTN7SOQ","short_pith_number":"pith:ZQ6BZXT5","schema_version":"1.0","canonical_sha256":"cc3c1cde7ddc0b7319dcd41c29b7f2741056ed316e4f71ecc46e4dee21d6eb9d","source":{"kind":"arxiv","id":"1312.4983","version":2},"attestation_state":"computed","paper":{"title":"Extreme slowdowns for one-dimensional excited random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson","submitted_at":"2013-12-17T21:37:09Z","abstract_excerpt":"We study the asymptotics of the probabilities of extreme slowdown events for transient one-dimensional excited random walks. That is, if $\\{X_n\\}_{n\\geq 0}$ is a transient one-dimensional excited random walk and $T_n = \\min\\{ k: \\, X_k = n\\}$, we study the asymptotics of probabilities of the form $P(X_n \\leq n^\\gamma)$ and $P(T_{n^\\gamma} \\geq n )$ with $\\gamma < 1$. We show that there is an interesting change in the rate of decay of these extreme slowdown probabilities when $\\gamma < 1/2$."},"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":"1312.4983","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2013-12-17T21:37:09Z","cross_cats_sorted":[],"title_canon_sha256":"e7fbddcbd53e70a85da69051031890e97467bcff473f69491528d1dbdbc2c186","abstract_canon_sha256":"664d58d0ea271aa06f2b1ab40e3060ccfe5f56c402ce99d419649abda8c6057f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:36.661765Z","signature_b64":"kQmIVdXaiMNGf0aLXECMS1UzfG1xrMTZJhN1gUbnCgxKZpu9x0SbSEWf8XNWCqFApUfB7Li3+oYc3yVx6acQCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"cc3c1cde7ddc0b7319dcd41c29b7f2741056ed316e4f71ecc46e4dee21d6eb9d","last_reissued_at":"2026-05-18T01:12:36.661091Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:36.661091Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Extreme slowdowns for one-dimensional excited random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Jonathon Peterson","submitted_at":"2013-12-17T21:37:09Z","abstract_excerpt":"We study the asymptotics of the probabilities of extreme slowdown events for transient one-dimensional excited random walks. That is, if $\\{X_n\\}_{n\\geq 0}$ is a transient one-dimensional excited random walk and $T_n = \\min\\{ k: \\, X_k = n\\}$, we study the asymptotics of probabilities of the form $P(X_n \\leq n^\\gamma)$ and $P(T_{n^\\gamma} \\geq n )$ with $\\gamma < 1$. We show that there is an interesting change in the rate of decay of these extreme slowdown probabilities when $\\gamma < 1/2$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.4983","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":""},"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":"1312.4983","created_at":"2026-05-18T01:12:36.661193+00:00"},{"alias_kind":"arxiv_version","alias_value":"1312.4983v2","created_at":"2026-05-18T01:12:36.661193+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1312.4983","created_at":"2026-05-18T01:12:36.661193+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZQ6BZXT53QFX","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZQ6BZXT53QFXGGO4","created_at":"2026-05-18T12:28:09.283467+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZQ6BZXT5","created_at":"2026-05-18T12:28:09.283467+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ","json":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ.json","graph_json":"https://pith.science/api/pith-number/ZQ6BZXT53QFXGGO42QOCTN7SOQ/graph.json","events_json":"https://pith.science/api/pith-number/ZQ6BZXT53QFXGGO42QOCTN7SOQ/events.json","paper":"https://pith.science/paper/ZQ6BZXT5"},"agent_actions":{"view_html":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ","download_json":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ.json","view_paper":"https://pith.science/paper/ZQ6BZXT5","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1312.4983&json=true","fetch_graph":"https://pith.science/api/pith-number/ZQ6BZXT53QFXGGO42QOCTN7SOQ/graph.json","fetch_events":"https://pith.science/api/pith-number/ZQ6BZXT53QFXGGO42QOCTN7SOQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ/action/storage_attestation","attest_author":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ/action/author_attestation","sign_citation":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ/action/citation_signature","submit_replication":"https://pith.science/pith/ZQ6BZXT53QFXGGO42QOCTN7SOQ/action/replication_record"}},"created_at":"2026-05-18T01:12:36.661193+00:00","updated_at":"2026-05-18T01:12:36.661193+00:00"}