Mass equidistribution for random polynomials
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.
Cite
@article{arxiv.1808.00932,
title = {Mass equidistribution for random polynomials},
author = {Turgay Bayraktar},
journal= {arXiv preprint arXiv:1808.00932},
year = {2020}
}
Comments
V3: Substantial revisions. Statement of the main result (now Theorem 1.1) is generalized for subgaussian coefficients. V4: is the final update to agree with the published version