{"paper":{"title":"Limiting empirical distribution of zeros and critical points of random polynomials agree in general","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Tulasi Ram Reddy","submitted_at":"2016-09-02T17:29:16Z","abstract_excerpt":"In this article, we study critical points (zeros of derivative) of random polynomials. Take two deterministic sequences $\\{a_n\\}_{n\\geq1}$ and $\\{b_n\\}_{n\\geq1}$ of complex numbers whose limiting empirical measures are same. By choosing $\\xi_n = a_n$ or $b_n$ with equal probability, define the sequence of polynomials by $P_n(z)=(z-\\xi_1)\\dots(z-\\xi_n)$. We show that the limiting measure of zeros and critical points agree for this sequence of random polynomials under some assumption. We also prove a similar result for triangular array of numbers. A similar result for zeros of generalized deriva"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.00675","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"}