Finite frames, frame potentials and determinantal point processes on the sphere

Abstract

Herein, we address the expectations of frame potentials of three types of determinantal point processes(DPPs) on the d-dimensional unit sphere: (i) spherical ensembles on the 2-dimensional unit sphere; (ii) harmonic ensembles on the d-dimensional unit sphere and (iii) jittered sampling point processes on the d-dimensional unit sphere. The random point configurations generated by such DPPs converge more rapidly towards finite unit norm tight frames(FUNTFs) than the Poisson point processes on the unit sphere.