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This is a Quantitative Study study.

October 13, 2025Open Access

Hyperuniformity and hyperfluctuations of random measures in commutative spaces

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The study establishes a bound on number variance for random measures in higher-rank matrix Lie groups, suggesting consistency across distributions.
A new definition of heat kernel hyperuniformity is introduced, generalizing previous concepts about random measures in Euclidean and hyperbolic spaces.
The relationship between Bartlett spectral measures and invariant Gaussian distributions is shown to enhance understanding of random distributions.
Spectral measures for determinantal point processes are computed, providing a spectral proof of hyperuniformity related to polyanalytic ensembles.

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This analysis explores hyperuniformity and Bartlett spectral measure in random distributions, indicating important connections to Gaussian processes.

Björklund et al. (2025) studied this question.

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This analysis explores hyperuniformity and Bartlett spectral measure in random distributions, indicating important connections to Gaussian processes.