{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2023:4CIQMEPS5TKMOGTKWUW65CC74S","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":"28ebfd6209c4f41596b3914145c8a956b4fe084d016e1e2a5afb4c8fdd2237bb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-12T21:07:43Z","title_canon_sha256":"f34726e7011cc6653b0d9b442ef9cde3f0e58f4af6b063c9d8c4b6f906a43edd"},"schema_version":"1.0","source":{"id":"2303.06756","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"2303.06756","created_at":"2026-07-05T09:37:49Z"},{"alias_kind":"arxiv_version","alias_value":"2303.06756v2","created_at":"2026-07-05T09:37:49Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.2303.06756","created_at":"2026-07-05T09:37:49Z"},{"alias_kind":"pith_short_12","alias_value":"4CIQMEPS5TKM","created_at":"2026-07-05T09:37:49Z"},{"alias_kind":"pith_short_16","alias_value":"4CIQMEPS5TKMOGTK","created_at":"2026-07-05T09:37:49Z"},{"alias_kind":"pith_short_8","alias_value":"4CIQMEPS","created_at":"2026-07-05T09:37:49Z"}],"graph_snapshots":[{"event_id":"sha256:58817f0396889846996fb68fed1b32d40a046730a5d7d11ef45feffd9e32e8e9","target":"graph","created_at":"2026-07-05T09:37:49Z","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"},"integrity":{"available":true,"clean":true,"detectors_run":[],"endpoint":"/pith/2303.06756/integrity.json","findings":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938","summary":{"advisory":0,"by_detector":{},"critical":0,"informational":0}},"paper":{"abstract_excerpt":"We study the asymptotic behaviour of a random walk whose evolution is dependent on the state of an itself dynamically evolving environment. In particular, we extend our previous results in [Bethuelsen and V\\\"ollering, 2016] and prove a strong law of large numbers and large deviation estimates assuming that the dynamic environment is \"path-cone\"-mixing. Under a mild assumption on the decay rate of this mixing property we further obtain a functional central limit theorem under the annealed law. Our method of proofs rest on the study of the so-called local environment process and general results ","authors_text":"Florian V\\\"ollering, Stein Andreas Bethuelsen","cross_cats":[],"headline":"","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-12T21:07:43Z","title":"Limit laws for random walks in a dynamic path-cone mixing random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2303.06756","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":"sha256:6eb72313f9aa0f0bfb5fe60dcde4c7b4a848bca86ad6bd14cb0c6135d1a112fd","target":"record","created_at":"2026-07-05T09:37:49Z","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":"28ebfd6209c4f41596b3914145c8a956b4fe084d016e1e2a5afb4c8fdd2237bb","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2023-03-12T21:07:43Z","title_canon_sha256":"f34726e7011cc6653b0d9b442ef9cde3f0e58f4af6b063c9d8c4b6f906a43edd"},"schema_version":"1.0","source":{"id":"2303.06756","kind":"arxiv","version":2}},"canonical_sha256":"e0910611f2ecd4c71a6ab52dee885fe4bd81ba02ed25b1a85f7aee256622f99e","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"e0910611f2ecd4c71a6ab52dee885fe4bd81ba02ed25b1a85f7aee256622f99e","first_computed_at":"2026-07-05T09:37:49.004907Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-07-05T09:37:49.004907Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"y/IpfmAuElP9GSf9Ax+7u2YN34BF96ItuYSuc8Aiepyn/JbZogvsqwZQWqjMHbbrKQvPN1f5wbJy0B1kIniRCQ==","signature_status":"signed_v1","signed_at":"2026-07-05T09:37:49.005427Z","signed_message":"canonical_sha256_bytes"},"source_id":"2303.06756","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:6eb72313f9aa0f0bfb5fe60dcde4c7b4a848bca86ad6bd14cb0c6135d1a112fd","sha256:58817f0396889846996fb68fed1b32d40a046730a5d7d11ef45feffd9e32e8e9"],"state_sha256":"099dad245e6730ad28869401bc53dbc1652762d4b0cf57cfb9bf8cd33f3904a6"}