{"paper":{"title":"Universality for zeros of random analytic functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.PR","authors_text":"Dmitry Zaporozhets, Zakhar Kabluchko","submitted_at":"2012-05-24T07:47:34Z","abstract_excerpt":"Let $\\xi_0,\\xi_1,...$ be independent identically distributed (i.i.d.) random variables such that $\\E \\log (1+|\\xi_0|)<\\infty$. We consider random analytic functions of the form $$ G_n(z)=\\sum_{k=0}^{\\infty} \\xi_k f_{k,n} z^k, $$ where $f_{k,n}$ are deterministic complex coefficients. Let $\\nu_n$ be the random measure assigning the same weight $1/n$ to each complex zero of $G_n$. Assuming essentially that $-\\frac 1n \\log f_{[tn], n}\\to u(t)$ as $n\\to\\infty$, where $u(t)$ is some function, we show that the measure $\\nu_n$ converges weakly to some deterministic measure which is characterized in t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1205.5355","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"}