Mass equidistribution for random polynomials

Bayraktar, Turgay (2019) Mass equidistribution for random polynomials. Potential Analysis . ISSN 0926-2601 (Print) 1572-929X (Online) Published Online First

There is a more recent version of this item available.
[thumbnail of This is a RoMEO green journal -- author can archive pre-print (ie pre-refereeing)] PDF (This is a RoMEO green journal -- author can archive pre-print (ie pre-refereeing))

Download (292kB)


The purpose of this note is to study asymptotic zero distribution of multivariate random polynomials as their degrees grow. For a smooth weight function with super logarithmic growth at infinity, we consider random linear combinations of associated orthogonal polynomials with subgaussian coefficients. This class of probability distributions contains a wide range of random variables including standard Gaussian and all bounded random variables. We prove that for almost every sequence of random polynomials their normalized zero currents become equidistributed with respect to a deterministic extremal current. The main ingredients of the proof are Bergman kernel asymptotics, mass equidistribution of random polynomials and concentration inequalities for subgaussian quadratic forms.
Item Type: Article
Subjects: Q Science > QA Mathematics > QA299.6-433 Analysis
Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
Divisions: Faculty of Engineering and Natural Sciences > Basic Sciences > Mathematics
Faculty of Engineering and Natural Sciences
Depositing User: Turgay Bayraktar
Date Deposited: 05 Dec 2019 14:48
Last Modified: 26 Apr 2022 10:13

Available Versions of this Item

Actions (login required)

View Item
View Item