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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Asymptotic normality of linear statistics of zeros of random polynomials
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by Turgay Bayraktar PDF
Proc. Amer. Math. Soc. 145 (2017), 2917-2929 Request permission

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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Additional Information
  • Turgay Bayraktar
  • Affiliation: Department of Mathematics, Syracuse University, Syracuse, New York 13244
  • Address at time of publication: Faculty of Engineering and Natural Sciences, Sabanci University, Istanbul, Turkey
  • MR Author ID: 1009679
  • Email: tbayrakt@syr.edu, tbayraktar@sabanciuniv.edu
  • Received by editor(s): March 2, 2016
  • Received by editor(s) in revised form: March 18, 2016, March 28, 2016, June 14, 2016, and August 2, 2016
  • Published electronically: December 30, 2016
  • Communicated by: Franc Forstneric
  • © Copyright 2016 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 145 (2017), 2917-2929
  • MSC (2010): Primary 32A60, 32A25; Secondary 60F05, 60D05
  • DOI: https://doi.org/10.1090/proc/13441
  • MathSciNet review: 3637941