A review of some recent results on random polynomials over R and over C

Details A review of some recent results on random polynomials over R and over C A review of some recent results on random polynomials over R and over C

2010-10-15

arxiv.org/abs/1010.3295v1

Mathematics

Probability

12 pages

Scientific paper

This article is divided in two parts. In the first part we review some recent results concerning the expected number of real roots of random system of polynomial equations. In the second part we deal with a different problem, namely, the distribution of the roots of certain complex random polynomials. We discuss a recent result in this direction, which shows that the associated points in the sphere (via the stereographic projection) are surprisingly well-suited with respect to the minimal logarithmic energy on the sphere.

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