{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:WRGN4CMILCOERQ336YKNLMHDXP","short_pith_number":"pith:WRGN4CMI","schema_version":"1.0","canonical_sha256":"b44cde0988589c48c37bf614d5b0e3bbe113d4c6f432f878ab7545d806f2e04d","source":{"kind":"arxiv","id":"1506.08541","version":1},"attestation_state":"computed","paper":{"title":"Anomalous recurrence properties of many-dimensional zero-drift random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aleksandar Mijatovi\\'c, Andrew R. Wade, Mikhail V. Menshikov, Nicholas Georgiou","submitted_at":"2015-06-29T08:35:16Z","abstract_excerpt":"Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \\in \\{1,2\\}$ but transient if $d \\geq 3$. Once spatial homogeneity is relaxed, this is no longer true. We study a family of zero-drift spatially non-homogeneous random walks (Markov processes) whose increment covariance matrix is asymptotically constant along rays from the origin, and which, in any ambient dimension $d \\geq 2$, can be adjusted so that the walk is either transient or recurrent. Natural examples are provided by rand"},"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":"1506.08541","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T08:35:16Z","cross_cats_sorted":[],"title_canon_sha256":"ab602825b715f3e20a5c48170e66b4abdf305e56cd8e0ba97aa18d0aaa62285a","abstract_canon_sha256":"e26ed38c17e0461c9a448d99a74f6888c3d232deda8c5ba60e7bc8c09d1b3431"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:53:21.107985Z","signature_b64":"QX2THzyThd4S7GvqTyy5Zdrpz3QiqYqFrbNVEcdDYDgTsYSOuFZr24bNfpLFAmUS0+VbHQaL5P2hs3UZYIKCBg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b44cde0988589c48c37bf614d5b0e3bbe113d4c6f432f878ab7545d806f2e04d","last_reissued_at":"2026-05-18T00:53:21.107484Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:53:21.107484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Anomalous recurrence properties of many-dimensional zero-drift random walks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Aleksandar Mijatovi\\'c, Andrew R. Wade, Mikhail V. Menshikov, Nicholas Georgiou","submitted_at":"2015-06-29T08:35:16Z","abstract_excerpt":"Famously, a $d$-dimensional, spatially homogeneous random walk whose increments are non-degenerate, have finite second moments, and have zero mean is recurrent if $d \\in \\{1,2\\}$ but transient if $d \\geq 3$. Once spatial homogeneity is relaxed, this is no longer true. We study a family of zero-drift spatially non-homogeneous random walks (Markov processes) whose increment covariance matrix is asymptotically constant along rays from the origin, and which, in any ambient dimension $d \\geq 2$, can be adjusted so that the walk is either transient or recurrent. Natural examples are provided by rand"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08541","kind":"arxiv","version":1},"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":"1506.08541","created_at":"2026-05-18T00:53:21.107565+00:00"},{"alias_kind":"arxiv_version","alias_value":"1506.08541v1","created_at":"2026-05-18T00:53:21.107565+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08541","created_at":"2026-05-18T00:53:21.107565+00:00"},{"alias_kind":"pith_short_12","alias_value":"WRGN4CMILCOE","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_16","alias_value":"WRGN4CMILCOERQ33","created_at":"2026-05-18T12:29:47.479230+00:00"},{"alias_kind":"pith_short_8","alias_value":"WRGN4CMI","created_at":"2026-05-18T12:29:47.479230+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/WRGN4CMILCOERQ336YKNLMHDXP","json":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP.json","graph_json":"https://pith.science/api/pith-number/WRGN4CMILCOERQ336YKNLMHDXP/graph.json","events_json":"https://pith.science/api/pith-number/WRGN4CMILCOERQ336YKNLMHDXP/events.json","paper":"https://pith.science/paper/WRGN4CMI"},"agent_actions":{"view_html":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP","download_json":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP.json","view_paper":"https://pith.science/paper/WRGN4CMI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1506.08541&json=true","fetch_graph":"https://pith.science/api/pith-number/WRGN4CMILCOERQ336YKNLMHDXP/graph.json","fetch_events":"https://pith.science/api/pith-number/WRGN4CMILCOERQ336YKNLMHDXP/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP/action/timestamp_anchor","attest_storage":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP/action/storage_attestation","attest_author":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP/action/author_attestation","sign_citation":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP/action/citation_signature","submit_replication":"https://pith.science/pith/WRGN4CMILCOERQ336YKNLMHDXP/action/replication_record"}},"created_at":"2026-05-18T00:53:21.107565+00:00","updated_at":"2026-05-18T00:53:21.107565+00:00"}