{"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"}