Zeros of polynomials with random coefficients

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 wit...

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Bibliographic Details
Published inJournal of approximation theory Vol. 189; pp. 88 - 100
Main Authors Pritsker, Igor E., Yeager, Aaron M.
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.01.2015
Subjects
Expected number of zeros
Polynomials
Random coefficients
Random orthogonal polynomials
Uniform distribution
Expected number of zeros
Uniform distribution
Polynomials
Random coefficients
Random orthogonal polynomials
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ISSN0021-9045
1096-0430
DOI10.1016/j.jat.2014.09.003

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Summary: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.
ISSN:0021-9045
1096-0430
DOI:10.1016/j.jat.2014.09.003