Box-covariances of hyperuniform point processes
Abstract
In this work, we present a complete characterization of the covariance structure of number statistics in boxes for hyperuniform point processes. Under a standard integrability assumption, the covariance depends solely on the overlap of the faces of the box. Beyond this assumption, a novel interpolating covariance structure emerges. This enables us to identify a limiting Gaussian ``coarse-grained'' process, counting the number of points in large boxes as a function of the box position. Depending on the integrability assumption, this process may be continuous or discontinuous, e.g.~in $d=1$ it is given by an increment process of a fractional Brownian motion.
Fields of Study & Subjects
Point processes and geometric inequalities
Publication details
- Journal / source
- Stochastic Processes and their Applications
- Publisher
- Elsevier BV
- Volume
- 199
- Pages
- 104996–104996
- Publication date
- 20 May 2026
- Language
- EN