{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2010:MDJIDEVWGGACUB4ARPRMFFL6CU","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":"8609f2492521ebedb60ec575b29a15e535ca927e28ba3e4008fa7432b0833d1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-15T13:59:50Z","title_canon_sha256":"02f34b962181172b60e749f3bac3521553ee466d40121a3f5fb1796b42395935"},"schema_version":"1.0","source":{"id":"1007.2565","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1007.2565","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"arxiv_version","alias_value":"1007.2565v3","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1007.2565","created_at":"2026-05-18T03:12:58Z"},{"alias_kind":"pith_short_12","alias_value":"MDJIDEVWGGAC","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_16","alias_value":"MDJIDEVWGGACUB4A","created_at":"2026-05-18T12:26:10Z"},{"alias_kind":"pith_short_8","alias_value":"MDJIDEVW","created_at":"2026-05-18T12:26:10Z"}],"graph_snapshots":[{"event_id":"sha256:f6543f04a7198382f35875914cbdb77ce8ec35dca0e31ce7474d469f576d019b","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 random Dirichlet environment (RWDE) which is a special type of random walks in random environment where the exit probabilities at each site are i.i.d. Dirichlet random variables. On ${\\mathbb Z}^d$, RWDE are parameterized by a 2d-uplet of positive reals called weights. In this paper, we characterize for $d\\ge 3$ the weights for which there exists an absolutely continuous invariant probability for the process viewed from the particle. We can deduce from this result and from [27] a complete description of the ballistic regime for $d\\ge 3$.","authors_text":"Christophe Sabot (ICJ)","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-15T13:59:50Z","title":"Random Dirichlet environment viewed from the particle in dimension $d\\ge 3$"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1007.2565","kind":"arxiv","version":3},"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":"sha256:604c7955bbfa0db1ddc27855a67040f2de0ed963cfb5b2e93772c70acd7d7ef9","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":"8609f2492521ebedb60ec575b29a15e535ca927e28ba3e4008fa7432b0833d1a","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2010-07-15T13:59:50Z","title_canon_sha256":"02f34b962181172b60e749f3bac3521553ee466d40121a3f5fb1796b42395935"},"schema_version":"1.0","source":{"id":"1007.2565","kind":"arxiv","version":3}},"canonical_sha256":"60d28192b631802a07808be2c2957e152c002e3a852b881fd2384dc6b019a187","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"60d28192b631802a07808be2c2957e152c002e3a852b881fd2384dc6b019a187","first_computed_at":"2026-05-18T03:12:58.259746Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:12:58.259746Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"SFHOcL3rMxznQ5F9JsKXK4ECRf/pTKQ46Iab25HqsZEBoSm2VOOGzTXLjfdhLLdL0L2ljNU/nHt3pV0QpkbyDQ==","signature_status":"signed_v1","signed_at":"2026-05-18T03:12:58.260482Z","signed_message":"canonical_sha256_bytes"},"source_id":"1007.2565","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:604c7955bbfa0db1ddc27855a67040f2de0ed963cfb5b2e93772c70acd7d7ef9","sha256:f6543f04a7198382f35875914cbdb77ce8ec35dca0e31ce7474d469f576d019b"],"state_sha256":"719533a7477b85811c30c52e712d7fce822289765293fbb356602a34039b8738"}