{"paper":{"title":"Roots of random polynomials whose coefficients have logarithmic tails","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":"2011-10-12T07:29:39Z","abstract_excerpt":"It has been shown by Ibragimov and Zaporozhets [In Prokhorov and Contemporary Probability Theory (2013) Springer] that the complex roots of a random polynomial $G_n(z)=\\sum_{k=0}^n\\xi_kz^k$ with i.i.d. coefficients $\\xi_0,\\ldots,\\xi_n$ concentrate a.s. near the unit circle as $n\\to\\infty$ if and only if ${\\mathbb{E}\\log_+}|\\xi_0|<\\infty$. We study the transition from concentration to deconcentration of roots by considering coefficients with tails behaving like $L({\\log}|t|)({\\log}|t|)^{-\\alpha}$ as $t\\to\\infty$, where $\\alpha\\geq0$, and $L$ is a slowly varying function. Under this assumption, "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.2585","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"}