Continuity of the asymptotics of expected zeros of fewnomials

2013/11/27 by Timothy Tran, Timothy C. Tran, Tran, Timothy
Mathematics · #Algebraic Geometry (math.AG) #Asymptotic distribution #Combinatorics #Complex Variables (math.CV) #Distribution (mathematics) #FOS: Mathematics #Geometry and complex manifolds #Infinity #Limiting #Mathematical Dynamics and Fractals #Mathematical analysis #Mathematics #Probability (math.PR) #Pure mathematics #Random variable #Statistics #Stochastic processes and statistical mechanics #math.AG #math.CV #math.PR

paper · pdf · doi:10.48550/arxiv.1311.7168

arxiv created 2013/11/27 · openalex publication_date 2013/11/27 · arxiv updated 2013/12/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06

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.

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