{"paper":{"title":"CLT for the zeros of Classical Random Trigonometric Polynomials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Federico Dalmao, Jean-Marc Aza\\\"is, Jos\\'e R. Le\\'on","submitted_at":"2014-01-22T18:12:26Z","abstract_excerpt":"We prove a Central Limit Theorem for the number of zeros of random trigonometric polynomials of the form $K^{-1/2}\\sum_{n=1}^{K} a_n\\cos(nt)$, being $(a_n)_n$ independent standard Gaussian random variables. In particular, we prove the conjecture by Farahmand, Granville & Wigman that the variance is equivalent to $V^2K$, $0<V^2<\\infty$, as $K\\to\\infty$. % The case of stationary trigonometric polynomials was studied by Granville & Wigman and by Aza\\\"\\is & Le\\'on. Our approach is based on the Hermite/Wiener-Chaos decomposition for square-integrable functionals of a Gaussian process and on Rice Fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.5745","kind":"arxiv","version":2},"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"}