{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:TETOTC6BK3GK33PAFBIOIHTCD3","short_pith_number":"pith:TETOTC6B","schema_version":"1.0","canonical_sha256":"9926e98bc156ccadede02850e41e621ed356901a62411e11a2d4124a437e0fb6","source":{"kind":"arxiv","id":"1102.5241","version":1},"attestation_state":"computed","paper":{"title":"A self-similar process arising from a random walk with random environment in random scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Brice Franke, Tatsuhiko Saigo","submitted_at":"2011-02-25T13:27:03Z","abstract_excerpt":"In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an i.i.d. scenery along its path. We assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem. The resulting limit process is a self-similar stochastic process with non-trivial dependencies."},"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":"1102.5241","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.ST","submitted_at":"2011-02-25T13:27:03Z","cross_cats_sorted":["stat.TH"],"title_canon_sha256":"7424e3bc6f10c41535907695294c8ff9aa138d72e69ed3d06406d037233c28f2","abstract_canon_sha256":"03578847d866c113cccd5db150f9a4103fac3c0b26435a077fbd2460f58add40"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:55.873204Z","signature_b64":"gNT2YgACj7XXfxgDSyduzCRjKFkw0V81gRg6uyRlTMejN3x/jw8+f2unJ7141E6sJGkPFToM5qEdbYj/5a+YCQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"9926e98bc156ccadede02850e41e621ed356901a62411e11a2d4124a437e0fb6","last_reissued_at":"2026-05-18T04:27:55.872554Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:55.872554Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A self-similar process arising from a random walk with random environment in random scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Brice Franke, Tatsuhiko Saigo","submitted_at":"2011-02-25T13:27:03Z","abstract_excerpt":"In this article, we merge celebrated results of Kesten and Spitzer [Z. Wahrsch. Verw. Gebiete 50 (1979) 5-25] and Kawazu and Kesten [J. Stat. Phys. 37 (1984) 561-575]. A random walk performs a motion in an i.i.d. environment and observes an i.i.d. scenery along its path. We assume that the scenery is in the domain of attraction of a stable distribution and prove that the resulting observations satisfy a limit theorem. The resulting limit process is a self-similar stochastic process with non-trivial dependencies."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5241","kind":"arxiv","version":1},"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":"1102.5241","created_at":"2026-05-18T04:27:55.872673+00:00"},{"alias_kind":"arxiv_version","alias_value":"1102.5241v1","created_at":"2026-05-18T04:27:55.872673+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1102.5241","created_at":"2026-05-18T04:27:55.872673+00:00"},{"alias_kind":"pith_short_12","alias_value":"TETOTC6BK3GK","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_16","alias_value":"TETOTC6BK3GK33PA","created_at":"2026-05-18T12:26:42.757692+00:00"},{"alias_kind":"pith_short_8","alias_value":"TETOTC6B","created_at":"2026-05-18T12:26:42.757692+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/TETOTC6BK3GK33PAFBIOIHTCD3","json":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3.json","graph_json":"https://pith.science/api/pith-number/TETOTC6BK3GK33PAFBIOIHTCD3/graph.json","events_json":"https://pith.science/api/pith-number/TETOTC6BK3GK33PAFBIOIHTCD3/events.json","paper":"https://pith.science/paper/TETOTC6B"},"agent_actions":{"view_html":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3","download_json":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3.json","view_paper":"https://pith.science/paper/TETOTC6B","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1102.5241&json=true","fetch_graph":"https://pith.science/api/pith-number/TETOTC6BK3GK33PAFBIOIHTCD3/graph.json","fetch_events":"https://pith.science/api/pith-number/TETOTC6BK3GK33PAFBIOIHTCD3/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3/action/timestamp_anchor","attest_storage":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3/action/storage_attestation","attest_author":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3/action/author_attestation","sign_citation":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3/action/citation_signature","submit_replication":"https://pith.science/pith/TETOTC6BK3GK33PAFBIOIHTCD3/action/replication_record"}},"created_at":"2026-05-18T04:27:55.872673+00:00","updated_at":"2026-05-18T04:27:55.872673+00:00"}