Voronoi and Voids Statistics for Super-homogeneous Point Processes

Abstract

We study the Voronoi and void statistics of super-homogeneous (or hyperuniform) point patterns in which the infinite-wavelength density fluctuations vanish. Super-homogeneous or hyperuniform point patterns arise in one-component plasmas, primordial density fluctuations in the Universe, and in jammed hard-particle packings. We specifically analyze a certain one-dimensional model by studying size fluctuations and correlations of the associated Voronoi cells. We derive exact results for the complete joint statistics of the size of two Voronoi cells. We also provide a sum rule that the correlation matrix for the Voronoi cells must obey in any space dimension. In contrast to the conventional picture of super-homogeneous systems, we show that infinitely large Voronoi cells or voids can exist in super-homogeneous point processes in any dimension. We also present two heuristic conditions to identify and classify any super-homogeneous point process in terms of the asymptotic behavior of the void size distribution.

27 pages, and 4 figures

References in corpus (4)

• Local Density Fluctuations, Hyperuniformity, and Order Metrics
• The Glass-like Universe: Real-space correlation properties of standard cosmological models
• Generation of Primordial Cosmological Perturbations from Statistical Mechanical Models
• Fluctuations in galaxy counts: a new test for homogeneity versus fractality

Cited by in corpus (20)

• A density-independent glass transition in biological tissues
• Hyperuniform States of Matter
• Classical Disordered Ground States: Super-Ideal Gases, and Stealth and Equi-Luminous Materials
• Point processes in arbitrary dimension from fermionic gases, random matrix theory, and number theory
• Statistical properties of determinantal point processes in high-dimensional Euclidean spaces
• Ground states of stealthy hyperuniform potentials: I. Entropically favored configurations
• Hyperuniformity, quasi-long-range correlations, and void-space constraints in maximally random jammed particle packings. I. Polydisperse spheres
• Stone-Wales Defects Preserve Hyperuniformity in Amorphous Two-Dimensional Materials
• Anomalous local coordination, density fluctuations, and void statistics in disordered hyperuniform many-particle ground states
• Structural Characterization of Many-Particle Systems on Approach to Hyperuniform States
• Enhanced Pinning For Vortices in Hyperuniform Substrates and Emergent Hyperuniform Vortex States
• Cloaking the Underlying Long-Range Order of Randomly Perturbed Lattices
• Nearly hyperuniform, nonhyperuniform, and antihyperuniform density fluctuations in two-dimensional transition metal dichalcogenides with defects
• Tilings of space and superhomogeneous point processes
• Quantum criticality in Ising chains with random hyperuniform couplings
• Dynamic Measure of Hyperuniformity and Nonhyperuniformity in Heterogeneous Media via the Diffusion Spreadability
• Static Structural Signatures of Nearly Jammed Disordered and Ordered Hard-Sphere Packings: Direct Correlation Function
• Fast Generation of Spectrally-Shaped Disorder
• Walkers on the circle
• Quantifying when hyperuniformity of a many-particle system leads to uniformity across length scales