Asymptotic normality of linear statistics of zeros of random polynomials

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Bayraktar, Turgay (2017) Asymptotic normality of linear statistics of zeros of random polynomials. Proceedings of the American Mathematical Society, 145 (7). pp. 2917-2929. ISSN 0002-9939 (Print) 1088-6826 (Online)

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Abstract

In this note, we prove a central limit theorem for smooth linear statistics of zeros of random polynomials which are linear combinations of orthogonal polynomials with iid standard complex Gaussian coefficients. Along the way, we obtain Bergman kernel asymptotics for weighted L-2-space of polynomials endowed with varying measures of the form e-(2n phi n(z)) dz under suitable assumptions on the weight functions phi(n).
Item Type: Article
Uncontrolled Keywords: Central limit theorem; linear statistics; random polynomial; Bergman kernel asymptotics
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Turgay Bayraktar
Date Deposited: 22 May 2017 14:46
Last Modified: 22 May 2019 13:50
URI: https://research.sabanciuniv.edu/id/eprint/32241

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