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arXiv · 1604.02007

Asymptotic normality of linear statistics of zeros of random polynomials

Turgay Bayraktar
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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 $e^{-2n\varphi_n(z)}dz$ under suitable assumptions on the weight functions $\varphi_n$.

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Turgay Bayraktar. 2016-04-07. Asymptotic normality of linear statistics of zeros of random polynomials. https://doi.org/10.1090/proc/13441

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