  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.
