Mass Equidistribution for Random Polynomials

  • Turgay BayraktarEmail author


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.


Random polynomial Equidistribution of zeros Equilibrium measure Global extremal function Bergman kernel asymptotics 

Mathematics Subject Classification (2010)

32A60 32A25 60D05 


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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Faculty of Engineering and Natural SciencesSabanci UniversityİstanbulTurkey

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