Continuity of the asymptotics of expected zeros of fewnomials

TL;DR

This paper explores the asymptotic behavior of expected zeros of random fewnomials, showing the limiting distribution is a continuous (k,k)-form, extending previous results on complex zeros of random polynomial systems.

Contribution

It demonstrates that the limiting expected zero distribution for random fewnomials has continuous coefficients, refining prior asymptotic formulas.

Findings

The limiting expected zero distribution is a (k,k)-form with continuous coefficients.

The result extends previous work on the asymptotics of zeros of random polynomial systems.

The paper confirms the continuity of the limiting form's coefficients.

Abstract

In "Random complex fewnomials, I," B. Shiffman and S. Zelditch determine the limiting formula as N goes to infinity of the (normalized) expected distribution of complex zeros of a system of k random n-nomials in m variables where the coefficients are taken from the SU(m+1) ensemble and the spectra are chosen uniformly at random. We recall their result and show the limiting formula is a (k,k)-form with continuous coefficients.