A review of some recent results on random polynomials over \(\mathbb R\) and over \(\mathbb C\)

zbMATH Open1278.60086arXiv1010.3295MaRDI QIDQ2872727

Diego Armentano

Publication date: 15 January 2014

Published in: Publicaciones Matemáticas del Uruguay (Search for Journal in Brave)

Abstract: 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.

Full work available at URL: https://arxiv.org/abs/1010.3295

Mathematics Subject Classification ID

Stochastic processes (60G99)

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