{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2011:4AABRRSIOWORKJYL42SQ4NX5BA","short_pith_number":"pith:4AABRRSI","schema_version":"1.0","canonical_sha256":"e00018c648759d15270be6a50e36fd081dd170755c1de32519d06e6c65f2d1e9","source":{"kind":"arxiv","id":"1112.0658","version":1},"attestation_state":"computed","paper":{"title":"Renewal theorems for random walks in random scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fran\\c{c}oise P\\`ene (LM), Nadine Guillotin-Plantard (ICJ)","submitted_at":"2011-12-03T14:54:06Z","abstract_excerpt":"Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We suppose that the distributions of $X_1$ and $\\xi_0$ belong to the normal domain of attraction of strictly stable distributions with index $\\alpha\\in[1,2]$ and $\\beta\\in(0,2)$ respectively. We are interested in the asymptotic behaviour as $|a|$ goes to infinity of quantities of the form $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n-a)]$ (when $(Z_n)_n$ is transient) or $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n)-h(Z_n-"},"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":"1112.0658","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-12-03T14:54:06Z","cross_cats_sorted":[],"title_canon_sha256":"45ab8b565421d10498b03cc1a02901c71b65bb4762ec8aec569c8ec987762dcd","abstract_canon_sha256":"b06f9b634e79849788efe6b6497f6604325807b9b0f5e9c0ce9495c1a5536270"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:07:06.015947Z","signature_b64":"9EFbrJd/kOyK6hrR0Q//0A+TE2LnQHs8GUE/jkBGC5tHHmKRps6qZH6YnRAFlGHB2Qk84raY/b+SuvyzXWItAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e00018c648759d15270be6a50e36fd081dd170755c1de32519d06e6c65f2d1e9","last_reissued_at":"2026-05-18T04:07:06.015385Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:07:06.015385Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Renewal theorems for random walks in random scenery","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Fran\\c{c}oise P\\`ene (LM), Nadine Guillotin-Plantard (ICJ)","submitted_at":"2011-12-03T14:54:06Z","abstract_excerpt":"Random walks in random scenery are processes defined by $Z_n:=\\sum_{k=1}^n\\xi_{X_1+...+X_k}$, where $(X_k,k\\ge 1)$ and $(\\xi_y,y\\in\\mathbb Z)$ are two independent sequences of i.i.d. random variables. We suppose that the distributions of $X_1$ and $\\xi_0$ belong to the normal domain of attraction of strictly stable distributions with index $\\alpha\\in[1,2]$ and $\\beta\\in(0,2)$ respectively. We are interested in the asymptotic behaviour as $|a|$ goes to infinity of quantities of the form $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n-a)]$ (when $(Z_n)_n$ is transient) or $\\sum_{n\\ge 1}{\\mathbb E}[h(Z_n)-h(Z_n-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1112.0658","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":"1112.0658","created_at":"2026-05-18T04:07:06.015486+00:00"},{"alias_kind":"arxiv_version","alias_value":"1112.0658v1","created_at":"2026-05-18T04:07:06.015486+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1112.0658","created_at":"2026-05-18T04:07:06.015486+00:00"},{"alias_kind":"pith_short_12","alias_value":"4AABRRSIOWOR","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_16","alias_value":"4AABRRSIOWORKJYL","created_at":"2026-05-18T12:26:20.644004+00:00"},{"alias_kind":"pith_short_8","alias_value":"4AABRRSI","created_at":"2026-05-18T12:26:20.644004+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/4AABRRSIOWORKJYL42SQ4NX5BA","json":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA.json","graph_json":"https://pith.science/api/pith-number/4AABRRSIOWORKJYL42SQ4NX5BA/graph.json","events_json":"https://pith.science/api/pith-number/4AABRRSIOWORKJYL42SQ4NX5BA/events.json","paper":"https://pith.science/paper/4AABRRSI"},"agent_actions":{"view_html":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA","download_json":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA.json","view_paper":"https://pith.science/paper/4AABRRSI","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1112.0658&json=true","fetch_graph":"https://pith.science/api/pith-number/4AABRRSIOWORKJYL42SQ4NX5BA/graph.json","fetch_events":"https://pith.science/api/pith-number/4AABRRSIOWORKJYL42SQ4NX5BA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA/action/storage_attestation","attest_author":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA/action/author_attestation","sign_citation":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA/action/citation_signature","submit_replication":"https://pith.science/pith/4AABRRSIOWORKJYL42SQ4NX5BA/action/replication_record"}},"created_at":"2026-05-18T04:07:06.015486+00:00","updated_at":"2026-05-18T04:07:06.015486+00:00"}