{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:CUV23QCEQVJDSYVRJJUYU4NJV7","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":"dee4489bb92d623728a25937acb88a89f63a1913b6c4d59e6861eb8f421e9f54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-19T11:42:01Z","title_canon_sha256":"bb5144c6607d39c0bd9d0d8f1d6828f444307866a477d5c02880be8637aca853"},"schema_version":"1.0","source":{"id":"1806.07166","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1806.07166","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"arxiv_version","alias_value":"1806.07166v1","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1806.07166","created_at":"2026-05-17T23:42:48Z"},{"alias_kind":"pith_short_12","alias_value":"CUV23QCEQVJD","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_16","alias_value":"CUV23QCEQVJDSYVR","created_at":"2026-05-18T12:32:19Z"},{"alias_kind":"pith_short_8","alias_value":"CUV23QCE","created_at":"2026-05-18T12:32:19Z"}],"graph_snapshots":[{"event_id":"sha256:d50d1b536fa411a21e6cd7b2e39e32797cd2ea4e8a0407fc9f93598bdcf4da15","target":"graph","created_at":"2026-05-17T23:42:48Z","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":"We study the recurrence/transience phase transition for Markov chains on $\\mathbb{R}_+$, $\\mathbb{R}$, and $\\mathbb{R}^2$ whose increments have heavy tails with exponent in $(1,2)$ and asymptotically zero mean. This is the infinite-variance analogue of the classical Lamperti problem. On $\\mathbb{R}_+$, for example, we show that if the tail of the positive increments is about $c y^{-\\alpha}$ for an exponent $\\alpha \\in (1,2)$ and if the drift at $x$ is about $b x^{-\\gamma}$, then the critical regime has $\\gamma = \\alpha -1$ and recurrence/transience is determined by the sign of $b + c\\pi \\textr","authors_text":"Andrew R. Wade, Dimitri Petritis, Mikhail V. Menshikov, Nicholas Georgiou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-19T11:42:01Z","title":"Markov chains with heavy-tailed increments and asymptotically zero drift"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1806.07166","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:a639b278674948b9f7faea5185ce1fdd5d5496d126a399789062cf6cbfea3556","target":"record","created_at":"2026-05-17T23:42:48Z","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":"dee4489bb92d623728a25937acb88a89f63a1913b6c4d59e6861eb8f421e9f54","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2018-06-19T11:42:01Z","title_canon_sha256":"bb5144c6607d39c0bd9d0d8f1d6828f444307866a477d5c02880be8637aca853"},"schema_version":"1.0","source":{"id":"1806.07166","kind":"arxiv","version":1}},"canonical_sha256":"152badc04485523962b14a698a71a9afda02083ec0ed9b81bc87b26ed933cd9c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"152badc04485523962b14a698a71a9afda02083ec0ed9b81bc87b26ed933cd9c","first_computed_at":"2026-05-17T23:42:48.966727Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:42:48.966727Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"H3NUEQK5kXXvTPlv+nHi0g38bVJzXdQJi/y1SYSwNV2MojRirsRuIk+7AoKI16U4dgQ4skpVovpfviF2pSi1Dw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:42:48.967192Z","signed_message":"canonical_sha256_bytes"},"source_id":"1806.07166","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:a639b278674948b9f7faea5185ce1fdd5d5496d126a399789062cf6cbfea3556","sha256:d50d1b536fa411a21e6cd7b2e39e32797cd2ea4e8a0407fc9f93598bdcf4da15"],"state_sha256":"1f0579c0f2df4ebea81ec185d70fc91c43ba73a0145de9bffc27a0f131549633"}