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It is known that R will have a heavy-tailed distribution under several different sets of assumptions on the vector (Q,N,C_1,...,C_N). This paper investigates the settings where either Z_N = sum_{i=1}^N C_i or Q are regularly varying with index -alpha < -1 and E[sum_{i=1}^N C"},"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":"1108.3809","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2011-08-18T18:49:46Z","cross_cats_sorted":[],"title_canon_sha256":"302d3c316b7acd373ab53a29bf947a4d3d75a6ba23638e8340f82a0d18884c32","abstract_canon_sha256":"aa4e2bf7a3f79f2bf604c48b741c31299cc9b66c7361bf605a256e9bd4381bec"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:15:07.436773Z","signature_b64":"hsmyfV9jiqglCV5NhMSbGrKS2mZHUEDJ+KHeKU58JOJPUtDZBn7t9IR9EstMacR/rsAqWWHdkb2OUP1v4osRAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"972ddcb533d90b83597d6172a821b2c2a8a92020112d264ec0146b3e6ad92fc1","last_reissued_at":"2026-05-18T04:15:07.436087Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:15:07.436087Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tail behavior of solutions of linear recursions on trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Mariana Olvera-Cravioto","submitted_at":"2011-08-18T18:49:46Z","abstract_excerpt":"Consider the linear nonhomogeneous fixed point equation\n  R =_d sum_{i=1}^N C_i R_i + Q, where (Q,N,C_1,...,C_N) is a random vector with N in{0,1,2,3,...}U{infty}, {C_i}_{i=1}^N >= 0, P(|Q|>0) > 0, and {R_i}_{i=1}^N is a sequence of i.i.d. random variables independent of (Q,N,C_1,...,C_N) having the same distribution as R. It is known that R will have a heavy-tailed distribution under several different sets of assumptions on the vector (Q,N,C_1,...,C_N). This paper investigates the settings where either Z_N = sum_{i=1}^N C_i or Q are regularly varying with index -alpha < -1 and E[sum_{i=1}^N C"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.3809","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":"1108.3809","created_at":"2026-05-18T04:15:07.436192+00:00"},{"alias_kind":"arxiv_version","alias_value":"1108.3809v1","created_at":"2026-05-18T04:15:07.436192+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1108.3809","created_at":"2026-05-18T04:15:07.436192+00:00"},{"alias_kind":"pith_short_12","alias_value":"S4W5ZNJT3EFY","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_16","alias_value":"S4W5ZNJT3EFYGWL5","created_at":"2026-05-18T12:26:41.206345+00:00"},{"alias_kind":"pith_short_8","alias_value":"S4W5ZNJT","created_at":"2026-05-18T12:26:41.206345+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/S4W5ZNJT3EFYGWL5MFZKQINSYK","json":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK.json","graph_json":"https://pith.science/api/pith-number/S4W5ZNJT3EFYGWL5MFZKQINSYK/graph.json","events_json":"https://pith.science/api/pith-number/S4W5ZNJT3EFYGWL5MFZKQINSYK/events.json","paper":"https://pith.science/paper/S4W5ZNJT"},"agent_actions":{"view_html":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK","download_json":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK.json","view_paper":"https://pith.science/paper/S4W5ZNJT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1108.3809&json=true","fetch_graph":"https://pith.science/api/pith-number/S4W5ZNJT3EFYGWL5MFZKQINSYK/graph.json","fetch_events":"https://pith.science/api/pith-number/S4W5ZNJT3EFYGWL5MFZKQINSYK/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK/action/timestamp_anchor","attest_storage":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK/action/storage_attestation","attest_author":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK/action/author_attestation","sign_citation":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK/action/citation_signature","submit_replication":"https://pith.science/pith/S4W5ZNJT3EFYGWL5MFZKQINSYK/action/replication_record"}},"created_at":"2026-05-18T04:15:07.436192+00:00","updated_at":"2026-05-18T04:15:07.436192+00:00"}