The Diamond ensemble: a constructive set of points with small logarithmic energy

Abstract

We define a family of random sets of points, the Diamond ensemble, on the sphere ${\mathbb{S}}^2$ depending on several parameters. Its most important property is that, for some of these parameters, the asymptotic expected value of the logarithmic energy of the points can be computed rigorously and shown to attain very small values, quite close to the conjectured minimal value.