May 21, 2024Open Access

Hyperuniformity of random measures on Euclidean and hyperbolic spaces

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Number variance demonstrates dependence on the volume of Euclidean ball boundaries, marking an advancement in theoretical understanding.
The research indicates that random measures in hyperbolic spaces show significant variability, lacking hyperuniformity.
Investigation defines spectral hyperuniformity through the analysis of complementary series diffraction in hyperbolic contexts, with implications for randomness theory and geometric modeling. Evaluation reveals essential features of random measures affecting their spatial properties, indicating further study is needed.

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This investigation finds bounds on number variances in Euclidean and hyperbolic spaces, suggesting patterns in randomness.

Björklund et al. (2024) studied this question.

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