{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2015:WRGN4CMILCOERQ336YKNLMHDXP","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":"e26ed38c17e0461c9a448d99a74f6888c3d232deda8c5ba60e7bc8c09d1b3431","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T08:35:16Z","title_canon_sha256":"ab602825b715f3e20a5c48170e66b4abdf305e56cd8e0ba97aa18d0aaa62285a"},"schema_version":"1.0","source":{"id":"1506.08541","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1506.08541","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"arxiv_version","alias_value":"1506.08541v1","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1506.08541","created_at":"2026-05-18T00:53:21Z"},{"alias_kind":"pith_short_12","alias_value":"WRGN4CMILCOE","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_16","alias_value":"WRGN4CMILCOERQ33","created_at":"2026-05-18T12:29:47Z"},{"alias_kind":"pith_short_8","alias_value":"WRGN4CMI","created_at":"2026-05-18T12:29:47Z"}],"graph_snapshots":[{"event_id":"sha256:52ccec006713fbed08704e502416282c97e3de7d32cac80754e5b0710f10f0da","target":"graph","created_at":"2026-05-18T00:53:21Z","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":"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","authors_text":"Aleksandar Mijatovi\\'c, Andrew R. Wade, Mikhail V. Menshikov, Nicholas Georgiou","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T08:35:16Z","title":"Anomalous recurrence properties of many-dimensional zero-drift random walks"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08541","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":"sha256:67c74f9e92905bb4a264b8950cdc1764231ecabc6e1820dc57ced55fba1652fc","target":"record","created_at":"2026-05-18T00:53:21Z","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":"e26ed38c17e0461c9a448d99a74f6888c3d232deda8c5ba60e7bc8c09d1b3431","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2015-06-29T08:35:16Z","title_canon_sha256":"ab602825b715f3e20a5c48170e66b4abdf305e56cd8e0ba97aa18d0aaa62285a"},"schema_version":"1.0","source":{"id":"1506.08541","kind":"arxiv","version":1}},"canonical_sha256":"b44cde0988589c48c37bf614d5b0e3bbe113d4c6f432f878ab7545d806f2e04d","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b44cde0988589c48c37bf614d5b0e3bbe113d4c6f432f878ab7545d806f2e04d","first_computed_at":"2026-05-18T00:53:21.107484Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:53:21.107484Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"QX2THzyThd4S7GvqTyy5Zdrpz3QiqYqFrbNVEcdDYDgTsYSOuFZr24bNfpLFAmUS0+VbHQaL5P2hs3UZYIKCBg==","signature_status":"signed_v1","signed_at":"2026-05-18T00:53:21.107985Z","signed_message":"canonical_sha256_bytes"},"source_id":"1506.08541","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:67c74f9e92905bb4a264b8950cdc1764231ecabc6e1820dc57ced55fba1652fc","sha256:52ccec006713fbed08704e502416282c97e3de7d32cac80754e5b0710f10f0da"],"state_sha256":"9f87f453c3490fd3f397551127ed7298efc44a741dbed7eac1b9aa3d7c01c5e8"}