Hyperuniform point sets on the sphere: probabilistic aspects

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.

References in corpus (6)

• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• Energy and discrepancy of rotationally invariant determinantal point processes in high dimensional spheres
• Diameter bounded equal measure partitions of Ahlfors regular metric measure spaces
• Hyperuniform point sets on the sphere: deterministic constructions
• Spherical structure factor and classification of hyperuniformity on the sphere
• Hyperuniformity on spherical surfaces

Cited by in corpus (7)

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• Impact of Random Spatial Truncation and Reciprocal-Space Binning on the Detection of Hyperuniformity in Disordered Systems
• Global order parameters for particle distributions on the sphere
• Linear statistics of determinantal point processes and norm representations
• On a family of singular continuous measures related to the doubling map
• Precise Determination of the Long-Time Asymptotics of the Diffusion Spreadability of Two-Phase Media