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Mass equidistribution for random polynomials

Bayraktar, Turgay (2020) Mass equidistribution for random polynomials. Potential Analysis, 53 (4). pp. 1403-1421. ISSN 0926-2601 (Print) 1572-929X (Online)

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Official URL: http://dx.doi.org/10.1007/s11118-019-09811-w

Abstract

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
Uncontrolled Keywords:Random polynomial; Equidistribution of zeros; Equilibrium measure; Global extremal function; Bergman kernel asymptotics
Subjects:Q Science > QA Mathematics > QA299.6-433 Analysis
Q Science > QA Mathematics > QA273-280 Probabilities. Mathematical statistics
ID Code:41374
Deposited By:Turgay Bayraktar
Deposited On:22 Mar 2021 18:32
Last Modified:22 Mar 2021 18:32

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