Asymptotic normality of linear statistics of zeros of random polynomials
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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Official URL: http://dx.doi.org/10.1090/proc/13441
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).
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