On p-frame potentials of the Beltrán and Etayo point processes on the sphere

Abstract

We address the two novel types of point processes on the multidimensional sphere proposed by Beltrán and Etayo. First, for the point process on the odd-dimensional sphere introduced by Beltrán and Etayo (Constr. Approx., 2018), we give an explicit form of the expectation of the p-frame potential of the process and investigate its asymptotic behavior. Second, for the point processes, termed generalized spherical ensemble, on the even-dimensional sphere introduced by Beltrán and Etayo (J. Math. Anal. Appl., 2019), we provide an upper bound of the expectation of the p-frame potential of the process.