On $p$-frame potentials of determinantal point processes on the sphere

Abstract

This study investigates the expectations of the $p$-frame potentials of three typical types of determinantal point processes on the $d$-sphere: (i) spherical ensembles on the $2$-sphere; (ii) harmonic ensembles on the $d$-sphere; and (iii) jittered sampling point processes on the $d$-sphere. By the results, it can be expected that such determinantal point processes have asymptotically smaller expectations of $p$-frame potentials than those of Poisson point processes on the sphere with the same number of points.