A generalization of the spherical ensemble to even-dimensional spheres

In a recent article [1], Alishahi and Zamani discuss the spherical ensemble, a rotationally invariant determinantal point process on S2. In this paper we extend this process in a natural way to the 2d-dimensional sphere S2d. 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