{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2017:4J5B2ZMW5GJPXNI42NXCU76YBI","short_pith_number":"pith:4J5B2ZMW","schema_version":"1.0","canonical_sha256":"e27a1d6596e992fbb51cd36e2a7fd80a19585763c306f0b6155ebb98262a1438","source":{"kind":"arxiv","id":"1704.05829","version":2},"attestation_state":"computed","paper":{"title":"Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.PR","authors_text":"Dmitri Finkelshtein, Pasha Tkachov","submitted_at":"2017-04-19T17:23:33Z","abstract_excerpt":"We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular sub-exponential functions and use it to find an analogue of Kesten's bound for functions on $\\mathbb{R}^d$. The results are applied for the study of the fundamental solution to a nonlocal heat-equation."},"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":"1704.05829","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2017-04-19T17:23:33Z","cross_cats_sorted":["math.AP","math.CA"],"title_canon_sha256":"c90a2d011723a132b0fa59ff8970bbc8a76eee8ed87d0456e19f97ca7f6be7e1","abstract_canon_sha256":"cec83b2b47ac747f5b99ac9c7d455a99a19a854ef26fe317c164e04e81221612"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:44.772805Z","signature_b64":"bwFND1RrJq5HnfTDxmnQ2LmVY2hFt3/RRuNB6c8yfGVqGzxRArByqjoSO1LTtQjhjw7pfbyxj1efSaooWSJZBA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"e27a1d6596e992fbb51cd36e2a7fd80a19585763c306f0b6155ebb98262a1438","last_reissued_at":"2026-05-18T00:22:44.772267Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:44.772267Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kesten's bound for sub-exponential densities on the real line and its multi-dimensional analogues","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP","math.CA"],"primary_cat":"math.PR","authors_text":"Dmitri Finkelshtein, Pasha Tkachov","submitted_at":"2017-04-19T17:23:33Z","abstract_excerpt":"We study the tail asymptotic of sub-exponential probability densities on the real line. Namely, we show that the n-fold convolution of a sub-exponential probability density on the real line is asymptotically equivalent to this density times n. We prove Kesten's bound, which gives a uniform in n estimate of the n-fold convolution by the tail of the density. We also introduce a class of regular sub-exponential functions and use it to find an analogue of Kesten's bound for functions on $\\mathbb{R}^d$. The results are applied for the study of the fundamental solution to a nonlocal heat-equation."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.05829","kind":"arxiv","version":2},"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":"1704.05829","created_at":"2026-05-18T00:22:44.772358+00:00"},{"alias_kind":"arxiv_version","alias_value":"1704.05829v2","created_at":"2026-05-18T00:22:44.772358+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1704.05829","created_at":"2026-05-18T00:22:44.772358+00:00"},{"alias_kind":"pith_short_12","alias_value":"4J5B2ZMW5GJP","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_16","alias_value":"4J5B2ZMW5GJPXNI4","created_at":"2026-05-18T12:31:00.734936+00:00"},{"alias_kind":"pith_short_8","alias_value":"4J5B2ZMW","created_at":"2026-05-18T12:31:00.734936+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/4J5B2ZMW5GJPXNI42NXCU76YBI","json":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI.json","graph_json":"https://pith.science/api/pith-number/4J5B2ZMW5GJPXNI42NXCU76YBI/graph.json","events_json":"https://pith.science/api/pith-number/4J5B2ZMW5GJPXNI42NXCU76YBI/events.json","paper":"https://pith.science/paper/4J5B2ZMW"},"agent_actions":{"view_html":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI","download_json":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI.json","view_paper":"https://pith.science/paper/4J5B2ZMW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1704.05829&json=true","fetch_graph":"https://pith.science/api/pith-number/4J5B2ZMW5GJPXNI42NXCU76YBI/graph.json","fetch_events":"https://pith.science/api/pith-number/4J5B2ZMW5GJPXNI42NXCU76YBI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI/action/storage_attestation","attest_author":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI/action/author_attestation","sign_citation":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI/action/citation_signature","submit_replication":"https://pith.science/pith/4J5B2ZMW5GJPXNI42NXCU76YBI/action/replication_record"}},"created_at":"2026-05-18T00:22:44.772358+00:00","updated_at":"2026-05-18T00:22:44.772358+00:00"}