In a recent article , Alishahi and Zamani discuss the spherical ensemble, a rotationally invariant determinantal point process on . 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.
- Determinantal point processes
- Riesz energy
Etayo Rodriguez, M. D. U., & Beltran, C. (2019). A generalization of the spherical ensemble to even-dimensional spheres. Journal of mathematical analysis and applications, 475(2), 1073-1092. https://doi.org/10.1016/j.jmaa.2019.03.004