Hyperuniform point sets on the sphere: probabilistic aspects

TL;DR

This paper extends the concept of hyperuniformity to the sphere, analyzing various point processes and identifying which are hyperuniform, thus bridging structural properties between disorder and order.

Contribution

It generalizes hyperuniformity to spherical point sets and evaluates multiple processes, including the projective ensemble, for hyperuniformity.

Findings

Determinantal point processes are hyperuniform on the sphere

The projective ensemble is not hyperuniform

Hyperuniformity characterizes intermediate structural behavior

Abstract

The concept of hyperuniformity has been introduced by Torquato and Stillinger in 2003 as a notion to detect structural behaviour intermediate between amorphous disorder and crystalline order. The present paper studies a generalisation of this concept to the unit sphere. It is shown that several well studied determinantal point processes are hyperuniform, one recently introduced process, the projective ensemble, is shown not to be hyperuniform.