Zeros of polynomials with random coefficients

JOURNAL OF APPROXIMATION THEORY

卷:189

Article

Pritsker, Igor E.¹  Yeager, Aaron M.¹ 

[1] Oklahoma State Univ, Dept Math, Stillwater, OK 74078 USA

关键词: Polynomials;    Random coefficients;    Expected number of zeros;    Uniform distribution;    Random orthogonal polynomials;   

DOI  :  10.1016/j.jat.2014.09.003

来源: Elsevier

【 摘 要 】

Zeros of many ensembles of polynomials with random coefficients are asymptotically equidistributed near the unit circumference. We give quantitative estimates for such equidistribution in terms of the expected discrepancy and expected number of roots in various sets. This is done for polynomials with coefficients that may be dependent, and need not have identical distributions. We also study random polynomials spanned by various deterministic bases. (C) 2014 Elsevier Inc. All rights reserved.

【 授权许可】

Free