{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2016:GSDZUFSBGON3G6LS6GY6UMP5T3","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":"407d00edb326ac14c2dce5661b83dee6dc3f6a600243b8a3386ca5fc1e8d2724","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-14T01:38:18Z","title_canon_sha256":"da5563495e5db12369d008f3712d526a8552d055bc48c4b392b906c260f74748"},"schema_version":"1.0","source":{"id":"1603.04107","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1603.04107","created_at":"2026-05-18T01:17:32Z"},{"alias_kind":"arxiv_version","alias_value":"1603.04107v2","created_at":"2026-05-18T01:17:32Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1603.04107","created_at":"2026-05-18T01:17:32Z"},{"alias_kind":"pith_short_12","alias_value":"GSDZUFSBGON3","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_16","alias_value":"GSDZUFSBGON3G6LS","created_at":"2026-05-18T12:30:19Z"},{"alias_kind":"pith_short_8","alias_value":"GSDZUFSB","created_at":"2026-05-18T12:30:19Z"}],"graph_snapshots":[{"event_id":"sha256:c01f44a4910d049d8017bd5248a45ab003f8202f6be092073face5e7806729b8","target":"graph","created_at":"2026-05-18T01:17:32Z","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 introduce a family of stochastic processes on the integers, depending on a parameter $p \\in [0,1]$ and interpolating between the deterministic rotor walk (p=0) and the simple random walk (p=1/2). This p-rotor walk is not a Markov chain but it has a local Markov property: for each $x \\in \\mathbb{Z}$ the sequence of successive exits from $x$ is a Markov chain. The main result of this paper identifies the scaling limit of the p-rotor walk with two-sided i.i.d. initial rotors. The limiting process takes the form $\\sqrt{\\frac{1-p}{p}} X(t)$, where $X$ is a doubly perturbed Brownian motion, that ","authors_text":"Ecaterina Sava-Huss, Lionel Levine, Wilfried Huss","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-14T01:38:18Z","title":"Interpolating between random walk and rotor walk"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1603.04107","kind":"arxiv","version":2},"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":"sha256:1da698bdd24101b609705bbf5946417b7da05e343717e6945afd9217b0f0c35b","target":"record","created_at":"2026-05-18T01:17:32Z","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":"407d00edb326ac14c2dce5661b83dee6dc3f6a600243b8a3386ca5fc1e8d2724","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-03-14T01:38:18Z","title_canon_sha256":"da5563495e5db12369d008f3712d526a8552d055bc48c4b392b906c260f74748"},"schema_version":"1.0","source":{"id":"1603.04107","kind":"arxiv","version":2}},"canonical_sha256":"34879a1641339bb37972f1b1ea31fd9eca1178dce3755b5c44fd31ec5ccf505b","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"34879a1641339bb37972f1b1ea31fd9eca1178dce3755b5c44fd31ec5ccf505b","first_computed_at":"2026-05-18T01:17:32.387326Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T01:17:32.387326Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"OD2xbo2hKwbQb/41iDChcL22ECEUKUvnoCLBoR2qCYh3ulYURpvbMftEBhAJYHEvtgnzW/PjO0djobxm/YhfCA==","signature_status":"signed_v1","signed_at":"2026-05-18T01:17:32.388072Z","signed_message":"canonical_sha256_bytes"},"source_id":"1603.04107","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:1da698bdd24101b609705bbf5946417b7da05e343717e6945afd9217b0f0c35b","sha256:c01f44a4910d049d8017bd5248a45ab003f8202f6be092073face5e7806729b8"],"state_sha256":"3d53bbabdd099d30adb90ac6ce152be29787d615deaeb4b47759239977e7e99c"}