{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:NFJ5X353Z5REY2MDFXYWY6OLAB","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":"18e5d4cad0b27e0cfc7530f00095092680efe55f4e06ededb4cc76ba1d22f079","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-15T11:38:01Z","title_canon_sha256":"e0be0d29cdedb026c24b5cdb648d91aa67b9ff73328fb84b455f88d63c5df6eb"},"schema_version":"1.0","source":{"id":"1404.3874","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1404.3874","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"arxiv_version","alias_value":"1404.3874v1","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1404.3874","created_at":"2026-05-18T02:54:13Z"},{"alias_kind":"pith_short_12","alias_value":"NFJ5X353Z5RE","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_16","alias_value":"NFJ5X353Z5REY2MD","created_at":"2026-05-18T12:28:41Z"},{"alias_kind":"pith_short_8","alias_value":"NFJ5X353","created_at":"2026-05-18T12:28:41Z"}],"graph_snapshots":[{"event_id":"sha256:877909cee95d7c484678bdd8b817398edf6a188468734589511b87f50b13d27a","target":"graph","created_at":"2026-05-18T02:54:13Z","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":"This work is motivated by the study of some two-dimensional random walks in random environment (RWRE) with transition probabilities independent of one coordinate of the walk. These are non-reversible models and can not be treated by electrical network techniques. The proof of the recurrence of such RWRE needs new estimates for quenched return probabilities of a one-dimensional recurrent RWRE. We obtained these estimates by constructing suitable valleys for the potential. They imply that k independent walkers in the same one-dimensional (recurrent) environment will meet in the origin infinitely","authors_text":"Francoise Pene (LM), Michael Kochler, Nina Gantert","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-15T11:38:01Z","title":"On the recurrence of some random walks in random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.3874","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:ba80b4713b923873315b74fc19d717dc3ba2f0094fa4e27e4eab26d538b6ea32","target":"record","created_at":"2026-05-18T02:54:13Z","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":"18e5d4cad0b27e0cfc7530f00095092680efe55f4e06ededb4cc76ba1d22f079","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-04-15T11:38:01Z","title_canon_sha256":"e0be0d29cdedb026c24b5cdb648d91aa67b9ff73328fb84b455f88d63c5df6eb"},"schema_version":"1.0","source":{"id":"1404.3874","kind":"arxiv","version":1}},"canonical_sha256":"6953dbefbbcf624c69832df16c79cb0075b211998b0c7daec780d4348fd79ad8","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6953dbefbbcf624c69832df16c79cb0075b211998b0c7daec780d4348fd79ad8","first_computed_at":"2026-05-18T02:54:13.451335Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:54:13.451335Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"v5tKEifulW5cy0CvgYLWUAVgCqVQnonTbdavM3LaxOzZhUzldCt9d2kO+CBKTO3hUpiNcBcFZJ85tAege/5UAw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:54:13.452000Z","signed_message":"canonical_sha256_bytes"},"source_id":"1404.3874","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:ba80b4713b923873315b74fc19d717dc3ba2f0094fa4e27e4eab26d538b6ea32","sha256:877909cee95d7c484678bdd8b817398edf6a188468734589511b87f50b13d27a"],"state_sha256":"d5c77271c5707ecdb40557c42ba5cd33db968106c4353179a5ce7cba65ee7de1"}