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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"},"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":"1407.6523","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-07-24T10:53:24Z","cross_cats_sorted":[],"title_canon_sha256":"25e24a2b9c3823f5a62e92cff063fc53ad1840e42626f13ff8e8a5a962376eb4","abstract_canon_sha256":"362cb88d81a15d87cb960532dbc0ed7f885cb3d4da6bcc0725d997878582ece8"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:46:38.546044Z","signature_b64":"hHsFzuZajACkjKqLYisgr2G1A4N7PcYfF1PrjMOAwS4V1dyTin6xMSzKptCYu1ssf9fcy/ixkBhTsK3JK2/NCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2181db7f5c7a56761190b0fcb0f73f82688bd6412bb72d12dcba49254f8cecc6","last_reissued_at":"2026-05-18T02:46:38.545679Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:46:38.545679Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Asymptotic distribution of complex zeros of random analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","submitted_at":"2014-07-24T10:53:24Z","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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.6523","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":"1407.6523","created_at":"2026-05-18T02:46:38.545739+00:00"},{"alias_kind":"arxiv_version","alias_value":"1407.6523v1","created_at":"2026-05-18T02:46:38.545739+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1407.6523","created_at":"2026-05-18T02:46:38.545739+00:00"},{"alias_kind":"pith_short_12","alias_value":"EGA5W724PJLH","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_16","alias_value":"EGA5W724PJLHMEMQ","created_at":"2026-05-18T12:28:25.294606+00:00"},{"alias_kind":"pith_short_8","alias_value":"EGA5W724","created_at":"2026-05-18T12:28:25.294606+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/EGA5W724PJLHMEMQWD6LB5Z7QJ","json":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ.json","graph_json":"https://pith.science/api/pith-number/EGA5W724PJLHMEMQWD6LB5Z7QJ/graph.json","events_json":"https://pith.science/api/pith-number/EGA5W724PJLHMEMQWD6LB5Z7QJ/events.json","paper":"https://pith.science/paper/EGA5W724"},"agent_actions":{"view_html":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ","download_json":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ.json","view_paper":"https://pith.science/paper/EGA5W724","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1407.6523&json=true","fetch_graph":"https://pith.science/api/pith-number/EGA5W724PJLHMEMQWD6LB5Z7QJ/graph.json","fetch_events":"https://pith.science/api/pith-number/EGA5W724PJLHMEMQWD6LB5Z7QJ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ/action/storage_attestation","attest_author":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ/action/author_attestation","sign_citation":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ/action/citation_signature","submit_replication":"https://pith.science/pith/EGA5W724PJLHMEMQWD6LB5Z7QJ/action/replication_record"}},"created_at":"2026-05-18T02:46:38.545739+00:00","updated_at":"2026-05-18T02:46:38.545739+00:00"}