{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:VPJZ72MM4443RWR65IHOKCORQN","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"dd3b64d1ceca64f6c62bc06839f98e96fd9fce8c52394c28140cddf3712d3650","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-07T17:21:07Z","title_canon_sha256":"79499fc60b117f0564d91a22d1a1e4c239ba4d8e5f628ae503f336fc0994c833"},"schema_version":"1.0","source":{"id":"1408.1658","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1408.1658","created_at":"2026-05-18T02:18:23Z"},{"alias_kind":"arxiv_version","alias_value":"1408.1658v2","created_at":"2026-05-18T02:18:23Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1408.1658","created_at":"2026-05-18T02:18:23Z"},{"alias_kind":"pith_short_12","alias_value":"VPJZ72MM4443","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_16","alias_value":"VPJZ72MM4443RWR6","created_at":"2026-05-18T12:28:54Z"},{"alias_kind":"pith_short_8","alias_value":"VPJZ72MM","created_at":"2026-05-18T12:28:54Z"}],"graph_snapshots":[{"event_id":"sha256:62489265df525b811f552bf9dd0631cc16afb5e9deec3c529b820f715d328e98","target":"graph","created_at":"2026-05-18T02:18:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"Consider a sequence of i.i.d. random Lipschitz functions $\\{\\Psi_n\\}_{n \\geq 0}$. Using this sequence we can define a Markov chain via the recursive formula $R_{n+1} = \\Psi_{n+1}(R_n)$. It is a well known fact that under some mild moment assumptions this Markov chain has a unique stationary distribution. We are interested in the tail behaviour of this distribution in the case when $\\Psi_0(t) \\approx A_0t+B_0$. We will show that under subexponential assumptions on the random variable $\\log^+(A_0\\vee B_0)$ the tail asymptotic in question can be described using the integrated tail function of $\\l","authors_text":"Piotr Dyszewski","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-07T17:21:07Z","title":"Iterated Random Functions and Slowly Varying Tails"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.1658","kind":"arxiv","version":2},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:af33adcc84070005325e964a315c09d01b26190487b17798aaee1eaf0bec5266","target":"record","created_at":"2026-05-18T02:18:23Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"dd3b64d1ceca64f6c62bc06839f98e96fd9fce8c52394c28140cddf3712d3650","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-08-07T17:21:07Z","title_canon_sha256":"79499fc60b117f0564d91a22d1a1e4c239ba4d8e5f628ae503f336fc0994c833"},"schema_version":"1.0","source":{"id":"1408.1658","kind":"arxiv","version":2}},"canonical_sha256":"abd39fe98ce739b8da3eea0ee509d1836742c076ce6268ed5453148185a36203","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"abd39fe98ce739b8da3eea0ee509d1836742c076ce6268ed5453148185a36203","first_computed_at":"2026-05-18T02:18:23.739519Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:18:23.739519Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"70M9hOBCziMsMaLPSCzAWOkysjQnpxRwD7hjQdnwZbIhOEBcsiCL4MwAp0tFjGYv5eHbGBLxFTaWsMP7edePCQ==","signature_status":"signed_v1","signed_at":"2026-05-18T02:18:23.741373Z","signed_message":"canonical_sha256_bytes"},"source_id":"1408.1658","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:af33adcc84070005325e964a315c09d01b26190487b17798aaee1eaf0bec5266","sha256:62489265df525b811f552bf9dd0631cc16afb5e9deec3c529b820f715d328e98"],"state_sha256":"0c7b2321671eb55cae439d5b3d3b4ef23cc125bb00eadadf3908c9e5a479af7e"}