Minimizing the discrete logarithmic energy on the sphere: the role of random polynomials

Abstract. We prove that points in the sphere associated with roots of random polynomials via the stereographic projection are surprisingly well-suited with respect to the minimal logarithmic energy on the sphere. That is, roots of random polynomials provide a fairly good approximation to elliptic Fekete points. This paper deals with the problem of distributing points in the 2-dimensional sphere, in a way that the logarithmic energy is minimized. More precisely, let x1,..., xN ∈ R3, and let (0.1) V (x1,..., xN) = l