{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:2BEQZJRKATV4T6GCYPLEYH6ISZ","short_pith_number":"pith:2BEQZJRK","schema_version":"1.0","canonical_sha256":"d0490ca62a04ebc9f8c2c3d64c1fc89666942f69a576817696b875034565d2d4","source":{"kind":"arxiv","id":"1503.05175","version":3},"attestation_state":"computed","paper":{"title":"Return- and hitting-time distributions of small sets in infinite measure preserving systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Roland Zweim\\\"uller, Simon Rechberger","submitted_at":"2015-03-17T19:23:48Z","abstract_excerpt":"We study convergence of return- and hitting-time distributions of small sets $E_{k}$ with $\\mu(E_{k})\\rightarrow0$ in recurrent ergodic dynamical systems preserving an infinite measure $\\mu$. Some properties which are easy in finite measure situations break down in this null-recurrent setup. However, in the presence of a uniform set $Y$ with wandering rate regularly varying of index $1-\\alpha$ with $\\alpha\\in(0,1]$, there is a scaling function suitable for all subsets of $Y$. In this case, we show that return distributions for the $E_{k}$ converge iff the corresponding hitting time distributio"},"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":"1503.05175","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2015-03-17T19:23:48Z","cross_cats_sorted":[],"title_canon_sha256":"4e0bef62994ce655f071eec2ed68b2d5c12731adaefdb03089c4dfd5969ba64d","abstract_canon_sha256":"cc3b113f91faaf286a3ff8bbc111f6ff367eeb397a1849be3bd87ce3b847d363"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:06:44.168292Z","signature_b64":"FLcptVDxwuy3Jf9ihjEi4xfxXYouFyUv9ngYCFwxxopWNr8shszxD2nMGCFnGzmAFc8smCkQ2QB67qN7c+AqAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d0490ca62a04ebc9f8c2c3d64c1fc89666942f69a576817696b875034565d2d4","last_reissued_at":"2026-05-18T00:06:44.167950Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:06:44.167950Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Return- and hitting-time distributions of small sets in infinite measure preserving systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Roland Zweim\\\"uller, Simon Rechberger","submitted_at":"2015-03-17T19:23:48Z","abstract_excerpt":"We study convergence of return- and hitting-time distributions of small sets $E_{k}$ with $\\mu(E_{k})\\rightarrow0$ in recurrent ergodic dynamical systems preserving an infinite measure $\\mu$. Some properties which are easy in finite measure situations break down in this null-recurrent setup. However, in the presence of a uniform set $Y$ with wandering rate regularly varying of index $1-\\alpha$ with $\\alpha\\in(0,1]$, there is a scaling function suitable for all subsets of $Y$. In this case, we show that return distributions for the $E_{k}$ converge iff the corresponding hitting time distributio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.05175","kind":"arxiv","version":3},"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":"1503.05175","created_at":"2026-05-18T00:06:44.168006+00:00"},{"alias_kind":"arxiv_version","alias_value":"1503.05175v3","created_at":"2026-05-18T00:06:44.168006+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1503.05175","created_at":"2026-05-18T00:06:44.168006+00:00"},{"alias_kind":"pith_short_12","alias_value":"2BEQZJRKATV4","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_16","alias_value":"2BEQZJRKATV4T6GC","created_at":"2026-05-18T12:28:59.999130+00:00"},{"alias_kind":"pith_short_8","alias_value":"2BEQZJRK","created_at":"2026-05-18T12:28:59.999130+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/2BEQZJRKATV4T6GCYPLEYH6ISZ","json":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ.json","graph_json":"https://pith.science/api/pith-number/2BEQZJRKATV4T6GCYPLEYH6ISZ/graph.json","events_json":"https://pith.science/api/pith-number/2BEQZJRKATV4T6GCYPLEYH6ISZ/events.json","paper":"https://pith.science/paper/2BEQZJRK"},"agent_actions":{"view_html":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ","download_json":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ.json","view_paper":"https://pith.science/paper/2BEQZJRK","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1503.05175&json=true","fetch_graph":"https://pith.science/api/pith-number/2BEQZJRKATV4T6GCYPLEYH6ISZ/graph.json","fetch_events":"https://pith.science/api/pith-number/2BEQZJRKATV4T6GCYPLEYH6ISZ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ/action/storage_attestation","attest_author":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ/action/author_attestation","sign_citation":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ/action/citation_signature","submit_replication":"https://pith.science/pith/2BEQZJRKATV4T6GCYPLEYH6ISZ/action/replication_record"}},"created_at":"2026-05-18T00:06:44.168006+00:00","updated_at":"2026-05-18T00:06:44.168006+00:00"}