{"paper":{"title":"Random power series near the endpoint of the convergence interval","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Bal\\'azs Maga, P\\'eter Maga","submitted_at":"2017-09-12T06:56:07Z","abstract_excerpt":"In this paper, we are going to consider power series $$ \\sum_{n=1}^{\\infty} a_nx^n, $$ where the coefficients $a_n$ are chosen independently at random from a finite set with uniform distribution. We prove that if the expected value of the coefficients is positive (resp. negative), then $$ \\lim_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=\\infty\\qquad (\\text{resp. }\\lim_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=-\\infty) $$ with probability $1$. Also, if the expected value of the coefficients is $0$, then $$ \\limsup_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=\\infty,\\qquad \\liminf_{x\\to 1-}\\sum_{n=1}^{\\infty} a_nx^n=-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.03705","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"}