Random complex fewnomials, I

Bernard Shiffman; Steve Zelditch

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arXiv · 1011.3492

Random complex fewnomials, I

Bernard Shiffman·Steve Zelditch

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Abstract

We introduce several notions of `random fewnomials', i.e. random polynomials with a fixed number f of monomials of degree N. The f exponents are chosen at random and then the coefficients are chosen to be Gaussian random, mainly from the SU(m + 1) ensemble. The results give limiting formulas as N goes to infinity for the expected distribution of complex zeros of a system of k random fewnomials in m variables. When k = m, for SU(m + 1) polynomials, the limit is the Monge-Ampere measure of a toric Kaehler potential on CP^m obtained by averaging a `discrete Legendre transform' of the Fubini-Study symplectic potential at f points of the unit simplex in R^m.

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BibTeX RIS

Bernard Shiffman, Steve Zelditch. 2010-11-15. Random complex fewnomials, I. https://arxiv.org/abs/1011.3492

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