A generalization of the spherical ensemble to even-dimensional spheres

TL;DR

This paper extends the spherical ensemble to even-dimensional spheres and shows that the associated determinantal point process has low expected Riesz s-energy, indicating efficient point distributions.

Contribution

It generalizes the spherical ensemble to 2d-dimensional spheres and analyzes the energy properties of the resulting determinantal point process.

Findings

Expected Riesz s-energy is lower than known asymptotics for minimal energy.

The process maintains rotational invariance on higher-dimensional spheres.

Provides a new probabilistic model for point distributions on even-dimensional spheres.

Abstract

In a recent article, Alishahi and Zamani discuss the spherical ensemble, a rotationally invariant determinantal point process on the 2-sphere. In this paper we extend this process in a natural way to the 2d-dimensional sphere. We prove that the expected value of the Riesz s-energy associated to this determinantal point process has a reasonably low value compared to the known asymptotic expansion of the minimal Riesz s-energy.