Bayraktar, Turgay (2019) On global universality for zeros of random polynomials. Hacettepe Journal of Mathematics and Statistics, 48 (2). pp. 384398. ISSN 13035010
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Official URL: http://dx.doi.org/10.15672/HJMS.2017.525
Abstract
In this work, we study asymptotic zero distribution of random multivariable polynomials which are random linear combinations
$\sum_{j}a_jP_j(z)$ with i.i.d coefficients relative to a basis of orthonormal polynomials $\{P_j\}_j$ induced by a multicircular weight function $Q$ defined on $\C^m$ satisfying suitable smoothness and growth conditions. In complex dimension $m\geq3$, we prove that $\Bbb{E}[(\log(1+a_j))^m]<\infty$ is a necessary and sufficient condition for normalized zero currents of random polynomials to be almost surely asymptotic to the (deterministic) extremal current $\frac{i}{\pi}\partial\overline{\partial}V_{Q}.$ In addition, in complex dimension one, we consider random linear combinations of orthonormal polynomials with respect to a regular measure in the sense of Stahl \& Totik and we prove analogous results in this setting.
Item Type:  Article 

Uncontrolled Keywords:  Random polynomial; distribution of zeros; global universality 
Subjects:  Q Science > QA Mathematics > QA299.6433 Analysis Q Science > QA Mathematics 
Divisions:  Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics Faculty of Engineering and Natural Sciences 
Depositing User:  Turgay Bayraktar 
Date Deposited:  03 May 2019 11:19 
Last Modified:  26 Apr 2022 10:02 
URI:  https://research.sabanciuniv.edu/id/eprint/36981 
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On global universality for zeros of random polynomials. (deposited 11 Aug 2018 15:27)
 On global universality for zeros of random polynomials. (deposited 03 May 2019 11:19) [Currently Displayed]