Expected Riesz energy of some determinantal processes on flat tori

TL;DR

This paper calculates the average Riesz energy for points randomly placed on flat tori according to specific determinantal processes and identifies the process that minimizes the expected energy asymptotically.

Contribution

It introduces a method to compute expected Riesz energy for determinantal processes on flat tori and finds the optimal process for minimal asymptotic energy.

Findings

Identified the determinantal process with the lowest asymptotic Riesz energy.

Provided explicit formulas for expected Riesz energy of certain processes.

Compared different processes to determine optimal energy configurations.

Abstract

We compute the expected Riesz energy of random points on flat tori drawn from certain translation invariant determinantal processes and determine the process in the family providing the optimal asymptotic expected Riesz energy.