{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2008:6BVJNAKJP43JOMOP37JRBXSV2Z","short_pith_number":"pith:6BVJNAKJ","schema_version":"1.0","canonical_sha256":"f06a9681497f369731cfdfd310de55d66ffbfff71621179759a681c4c1c5d4ea","source":{"kind":"arxiv","id":"0812.1948","version":6},"attestation_state":"computed","paper":{"title":"A central limit theorem for random walk in random environment on marked Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gabriel Faraud","submitted_at":"2008-12-10T16:15:35Z","abstract_excerpt":"In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In the critical case, we obtain a criterion for the positive/null recurrence. Several regimes appear, as proved (in a similar model), by Y. Hu and Z. Shi (2007). We focus on the \"diffusive\" regime and improve their result in this case, by obtaining a functional Central Limit Theorem. Our result is also an extension of a result by Y. Peres and O. Zeitouni (2008), obtain"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0812.1948","kind":"arxiv","version":6},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2008-12-10T16:15:35Z","cross_cats_sorted":[],"title_canon_sha256":"99c6821bac30c162cff72a32b192bb8ab6bdd64b7379bebcd72a966d3b457e94","abstract_canon_sha256":"05303a3fd566842633b228faf3e448a7f247ec42e96904d2c53aa1037d5ce157"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:14:18.365697Z","signature_b64":"Ejrj1oHbarnL/N0YTEwVMz952UDGIarWYcNpllvORDyd9fxXBo39WHqiYOKJZTRrOk7Lw+OWNMs85yydh7Z8DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f06a9681497f369731cfdfd310de55d66ffbfff71621179759a681c4c1c5d4ea","last_reissued_at":"2026-05-18T04:14:18.365067Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:14:18.365067Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A central limit theorem for random walk in random environment on marked Galton-Watson trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Gabriel Faraud","submitted_at":"2008-12-10T16:15:35Z","abstract_excerpt":"In this article we focus on a general model of random walk on random marked trees. We prove a recurrence criterion, analogue to the recurrence criterion proved by R. Lyons and Robin Pemantle (1992) in a slightly different model. In the critical case, we obtain a criterion for the positive/null recurrence. Several regimes appear, as proved (in a similar model), by Y. Hu and Z. Shi (2007). We focus on the \"diffusive\" regime and improve their result in this case, by obtaining a functional Central Limit Theorem. Our result is also an extension of a result by Y. Peres and O. Zeitouni (2008), obtain"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0812.1948","kind":"arxiv","version":6},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"},"aliases":[{"alias_kind":"arxiv","alias_value":"0812.1948","created_at":"2026-05-18T04:14:18.365175+00:00"},{"alias_kind":"arxiv_version","alias_value":"0812.1948v6","created_at":"2026-05-18T04:14:18.365175+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0812.1948","created_at":"2026-05-18T04:14:18.365175+00:00"},{"alias_kind":"pith_short_12","alias_value":"6BVJNAKJP43J","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_16","alias_value":"6BVJNAKJP43JOMOP","created_at":"2026-05-18T12:25:56.245647+00:00"},{"alias_kind":"pith_short_8","alias_value":"6BVJNAKJ","created_at":"2026-05-18T12:25:56.245647+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z","json":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z.json","graph_json":"https://pith.science/api/pith-number/6BVJNAKJP43JOMOP37JRBXSV2Z/graph.json","events_json":"https://pith.science/api/pith-number/6BVJNAKJP43JOMOP37JRBXSV2Z/events.json","paper":"https://pith.science/paper/6BVJNAKJ"},"agent_actions":{"view_html":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z","download_json":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z.json","view_paper":"https://pith.science/paper/6BVJNAKJ","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0812.1948&json=true","fetch_graph":"https://pith.science/api/pith-number/6BVJNAKJP43JOMOP37JRBXSV2Z/graph.json","fetch_events":"https://pith.science/api/pith-number/6BVJNAKJP43JOMOP37JRBXSV2Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z/action/storage_attestation","attest_author":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z/action/author_attestation","sign_citation":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z/action/citation_signature","submit_replication":"https://pith.science/pith/6BVJNAKJP43JOMOP37JRBXSV2Z/action/replication_record"}},"created_at":"2026-05-18T04:14:18.365175+00:00","updated_at":"2026-05-18T04:14:18.365175+00:00"}