Bayraktar, Turgay (2019) On global universality for zeros of random polynomials. Hacettepe Journal of Mathematics and Statistics, 48 (2). pp. 384398. ISSN 13035010
This is the latest version of this item.
PDF
10._Universality.pdf
Download (236kB)
10._Universality.pdf
Download (236kB)
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:  31 Jul 2023 12:48 
URI:  https://research.sabanciuniv.edu/id/eprint/36981 
Available Versions of this Item

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]