{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:EGA5W724PJLHMEMQWD6LB5Z7QJ","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":"362cb88d81a15d87cb960532dbc0ed7f885cb3d4da6bcc0725d997878582ece8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T10:53:24Z","title_canon_sha256":"25e24a2b9c3823f5a62e92cff063fc53ad1840e42626f13ff8e8a5a962376eb4"},"schema_version":"1.0","source":{"id":"1407.6523","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1407.6523","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"arxiv_version","alias_value":"1407.6523v1","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6523","created_at":"2026-05-18T02:46:38Z"},{"alias_kind":"pith_short_12","alias_value":"EGA5W724PJLH","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_16","alias_value":"EGA5W724PJLHMEMQ","created_at":"2026-05-18T12:28:25Z"},{"alias_kind":"pith_short_8","alias_value":"EGA5W724","created_at":"2026-05-18T12:28:25Z"}],"graph_snapshots":[{"event_id":"sha256:5016e95b17665de735e9b81d6bf84d357d1ffbf1271842dbff4180d778aecfc6","target":"graph","created_at":"2026-05-18T02:46:38Z","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":"Let $\\xi_0,\\xi_1,\\ldots$ be independent identically distributed complex- valued random variables such that $\\mathbb{E}\\log(1+|\\xi _0|)<\\infty$. We consider random analytic functions of the form \\[\\mathbf{G}_n(z)=\\sum_{k=0}^{\\infty}\\xi_kf_{k,n}z^k,\\] where $f_{k,n}$ are deterministic complex coefficients. Let $\\mu_n$ be the random measure counting the complex zeros of $\\mathbf{G}_n$ according to their multiplicities. Assuming essentially that $-\\frac{1}{n}\\log f_{[tn],n}\\to u(t)$ as $n\\to\\infty$, where $u(t)$ is some function, we show that the measure $\\frac{1}{n}\\mu_n$ converges in probability","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T10:53:24Z","title":"Asymptotic distribution of complex zeros of random analytic functions"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6523","kind":"arxiv","version":1},"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":"sha256:81382b959e590e4ccb73ed35a73e718b06fe38ffb88150e03dd21bbc677aa932","target":"record","created_at":"2026-05-18T02:46:38Z","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":"362cb88d81a15d87cb960532dbc0ed7f885cb3d4da6bcc0725d997878582ece8","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T10:53:24Z","title_canon_sha256":"25e24a2b9c3823f5a62e92cff063fc53ad1840e42626f13ff8e8a5a962376eb4"},"schema_version":"1.0","source":{"id":"1407.6523","kind":"arxiv","version":1}},"canonical_sha256":"2181db7f5c7a56761190b0fcb0f73f82688bd6412bb72d12dcba49254f8cecc6","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"2181db7f5c7a56761190b0fcb0f73f82688bd6412bb72d12dcba49254f8cecc6","first_computed_at":"2026-05-18T02:46:38.545679Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:46:38.545679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"hHsFzuZajACkjKqLYisgr2G1A4N7PcYfF1PrjMOAwS4V1dyTin6xMSzKptCYu1ssf9fcy/ixkBhTsK3JK2/NCw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:46:38.546044Z","signed_message":"canonical_sha256_bytes"},"source_id":"1407.6523","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:81382b959e590e4ccb73ed35a73e718b06fe38ffb88150e03dd21bbc677aa932","sha256:5016e95b17665de735e9b81d6bf84d357d1ffbf1271842dbff4180d778aecfc6"],"state_sha256":"cbe405c27bfb732d925b8aec607b56b8286700fd3eb20955a5a972e47981a589"}