{"paper":{"title":"Random Bernstein-Markov factors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.PR"],"primary_cat":"math.CV","authors_text":"Igor Pritsker, Koushik Ramachandran","submitted_at":"2018-10-23T15:55:03Z","abstract_excerpt":"For a polynomial $P_n$ of degree $n$, Bernstein's inequality states that $\\|P_n'\\| \\le n \\|P_n\\|$ for all $L^p$ norms on the unit circle, $0<p\\le\\infty,$ with equality for $P_n(z)= c z^n.$ We study this inequality for random polynomials, and show that the expected (average) and almost sure value of $\\Vert P_n' \\Vert/\\Vert P_n\\Vert$ is often different from the classical deterministic upper bound $n$. In particular, for circles of radii less than one, the ratio $\\Vert P_n' \\Vert/\\Vert P_n\\Vert$ is almost surely bounded as $n$ tends to infinity, and its expected value is uniformly bounded for all"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1810.09931","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"}