{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2009:NW2TK2M46LMIR6LC6AQFH2A24T","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":"2caf68ccf4612a5b9dbc3f9fde6dc92c5ad587e7601d57d1ad177ba43435e2ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-24T20:12:12Z","title_canon_sha256":"2afff678ecdfa55a8bf2d1f1350855392488d2c7f621c801c96453c314aa0ed4"},"schema_version":"1.0","source":{"id":"0905.3917","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"0905.3917","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"0905.3917v2","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0905.3917","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"NW2TK2M46LMI","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_16","alias_value":"NW2TK2M46LMIR6LC","created_at":"2026-05-18T12:26:00Z"},{"alias_kind":"pith_short_8","alias_value":"NW2TK2M4","created_at":"2026-05-18T12:26:00Z"}],"graph_snapshots":[{"event_id":"sha256:486d47a01d3e3de5bd04b4554c7d3c40e44700a261f0d0675fc0dd4ff7c7e3f2","target":"graph","created_at":"2026-05-18T03:12:58Z","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 consider random walks in a random environment that is given by i.i.d. Dirichlet distributions at each vertex of Z^d or, equivalently, oriented edge reinforced random walks on Z^d. The parameters of the distribution are a 2d-uplet of positive real numbers indexed by the unit vectors of Z^d. We prove that, as soon as these weights are nonsymmetric, the random walk in this random environment is transient in a direction with positive probability. In dimension 2, this result can be strenghened to an almost sure directional transience thanks to the 0-1 law from [ZM01]. Our proof relies on the pro","authors_text":"Christophe Sabot (ICJ), Laurent Tournier (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-24T20:12:12Z","title":"Reversed Dirichlet environment and directional transience of random walks in Dirichlet random environment"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0905.3917","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":"sha256:31a4d7b48e4d00884f150ddfcac281d6fe676095a45ac249e075b8c7f523828a","target":"record","created_at":"2026-05-18T03:12:58Z","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":"2caf68ccf4612a5b9dbc3f9fde6dc92c5ad587e7601d57d1ad177ba43435e2ff","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2009-05-24T20:12:12Z","title_canon_sha256":"2afff678ecdfa55a8bf2d1f1350855392488d2c7f621c801c96453c314aa0ed4"},"schema_version":"1.0","source":{"id":"0905.3917","kind":"arxiv","version":2}},"canonical_sha256":"6db535699cf2d888f962f02053e81ae4da0b3df9e0c6ce1cfb9d5b4e71791717","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"6db535699cf2d888f962f02053e81ae4da0b3df9e0c6ce1cfb9d5b4e71791717","first_computed_at":"2026-05-18T03:12:58.311051Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.311051Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"FOxZV1Why/KiTl5WUs040E79gy8YnWObXGbFPsf56mD3UoDYKY6hgRusVFUuSp33NnfOsshxQPZN8ddbCg/ACw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.311939Z","signed_message":"canonical_sha256_bytes"},"source_id":"0905.3917","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:31a4d7b48e4d00884f150ddfcac281d6fe676095a45ac249e075b8c7f523828a","sha256:486d47a01d3e3de5bd04b4554c7d3c40e44700a261f0d0675fc0dd4ff7c7e3f2"],"state_sha256":"23f237b33539f5737cfab84978346174659202427e898d83ec4d0277acfe4edc"}